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The image shows the calendar of a month of a particular non-leap year. Which day of the week was on September 5 of that year? | [
"Tuesday",
"Sunday",
"Monday",
"Wednesday"
] | Sunday | {'image_year': 2590, 'image_month': [12, 'December'], 'query_year': 2590, 'query_month': [9, 'September'], 'query_day': 5} |
|
The image shows the calendar of a month of a particular non-leap year. Which day of the week was on November 2 of that year? | [
"Saturday",
"Thursday",
"Monday",
"Friday"
] | Saturday | {'image_year': 2622, 'image_month': [9, 'September'], 'query_year': 2622, 'query_month': [11, 'November'], 'query_day': 2} |
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A checker game is being played on a grid of 4 squares with 2 green and 1 red checkers. Initially, the checkers are arranged as shown in the starting configuration with the 3 checkers occupying 3 squares and one unoccupied square. Green checkers only move rightward and red checkers only move leftward. Every move is either i) a slide to the adjacent empty square, or ii) a jump over one position to an empty square, provided the checker being jumped over is of a different colour. Each square can accommodate a maximum of one checker at any time. How many moves are required to reach the ending configuration from the starting configuration following the specified rules? | [
"2",
"4",
"5",
"3"
] | 5 | {'start_position': 'GG_R', 'end_position': 'R_GG', 'green_checkers': 2, 'red_checkers': 1, 'moves': ['GG_R', 'G_GR', 'GRG_', 'GR_G', '_RGG', 'R_GG']} |
|
Sarah came to an event 2 hours 25 minutes ago. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What was the time when Sarah came to the event? | [
"9:13",
"10:39",
"8:36",
"4:03"
] | 8:36 | {'current_hour': 11, 'current_minute': 1, 'subtract_hour': 2, 'subtract_minute': 25} |
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A storekeeper is a puzzle in which the player pushes boxes around in a warehouse trying to get them to target locations. The game is represented by an 6 x 6 grid of characters grid where each element is a wall, floor, or box. Your task is to move the box to the end flag under the following rules:
1. The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box by 1 grid. This is a push.
2. The player cannot walk through the box.
What is the minimum number of pushes to move the box to the end flag. | [
"1",
"4",
"5",
"2"
] | 4 | {'ids': {'empty': '.', 'brick': '#', 'box': 'B', 'person': 'S', 'target': 'T'}, 'timestep': {'grid_0': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '.', '.', '#'], ['#', '.', 'B', '.', '.', '#'], ['#', 'S', '.', '#', '.', '#'], ['#', '.', '.', '.', 'T', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_1': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '.', '.', '#'], ['#', '.', 'S', '.', '.', '#'], ['#', '', 'B', '#', '.', '#'], ['#', '.', '.', '.', 'T', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_2': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '.', '.', '#'], ['#', '.', '', '.', '.', '#'], ['#', '', 'S', '#', '.', '#'], ['#', '.', 'B', '.', 'T', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_3': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '.', '.', '#'], ['#', '.', '', '.', '.', '#'], ['#', '', '.', '#', '.', '#'], ['#', '.', 'S', 'B', 'T', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_4': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '.', '.', '#'], ['#', '.', '', '.', '.', '#'], ['#', '', '.', '#', '.', '#'], ['#', '.', '.', 'S', 'B', '#'], ['#', '#', '#', '#', '#', '#']]}, 'target': [4, 4], 'box_location': [[2, 2], [3, 2], [4, 2], [4, 3], [4, 4]]} |
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The board shown in the image is a sliding puzzle of 4 * 4 tile dimensions. It has 15 numbered tiles and one unoccupied (open) position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. All tiles always stay and move inside the red boundary wall, as shown in the image. A move is defined as moving the open position by one tile unit in any available direction. You start from the board position shown in the image and perform exactly 3 moves. What is the minimum sum that you can achieve across the left most column in the final board position? | [
"23",
"10",
"40",
"17"
] | 23 | {'starting_grid': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 0, 6, 15]], 'total_moves': 3, 'path_track': {'left, right, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], 'left, right, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], 'left, right, up': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], 'left, up, right': [[10, 14, 3, 1], [5, 4, 2, 12], [11, 0, 13, 7], [9, 8, 6, 15]], 'left, up, up': [[10, 14, 3, 1], [0, 4, 2, 12], [5, 11, 13, 7], [9, 8, 6, 15]], 'left, up, down': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], 'right, left, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], 'right, left, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], 'right, left, up': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], 'right, right, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], 'right, right, up': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 0], [8, 6, 15, 7]], 'right, up, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 11, 7], [8, 6, 13, 15]], 'right, up, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 7, 0], [8, 6, 13, 15]], 'right, up, up': [[10, 14, 3, 1], [5, 4, 0, 12], [9, 11, 2, 7], [8, 6, 13, 15]], 'right, up, down': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], 'up, left, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], 'up, left, up': [[10, 14, 3, 1], [0, 4, 2, 12], [5, 9, 13, 7], [8, 11, 6, 15]], 'up, left, down': [[10, 14, 3, 1], [5, 4, 2, 12], [8, 9, 13, 7], [0, 11, 6, 15]], 'up, right, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], 'up, right, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 13, 7, 0], [8, 11, 6, 15]], 'up, right, up': [[10, 14, 3, 1], [5, 4, 0, 12], [9, 13, 2, 7], [8, 11, 6, 15]], 'up, right, down': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 13, 6, 7], [8, 11, 0, 15]], 'up, up, left': [[10, 14, 3, 1], [0, 5, 2, 12], [9, 4, 13, 7], [8, 11, 6, 15]], 'up, up, right': [[10, 14, 3, 1], [5, 2, 0, 12], [9, 4, 13, 7], [8, 11, 6, 15]], 'up, up, up': [[10, 0, 3, 1], [5, 14, 2, 12], [9, 4, 13, 7], [8, 11, 6, 15]], 'up, up, down': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], 'up, down, left': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], 'up, down, right': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], 'up, down, up': [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]]}, 'possible_states': [[[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [11, 0, 13, 7], [9, 8, 6, 15]], [[10, 14, 3, 1], [0, 4, 2, 12], [5, 11, 13, 7], [9, 8, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 0], [8, 6, 15, 7]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 11, 7], [8, 6, 13, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 7, 0], [8, 6, 13, 15]], [[10, 14, 3, 1], [5, 4, 0, 12], [9, 11, 2, 7], [8, 6, 13, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [0, 4, 2, 12], [5, 9, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [8, 9, 13, 7], [0, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 13, 7, 0], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 0, 12], [9, 13, 2, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 13, 6, 7], [8, 11, 0, 15]], [[10, 14, 3, 1], [0, 5, 2, 12], [9, 4, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 2, 0, 12], [9, 4, 13, 7], [8, 11, 6, 15]], [[10, 0, 3, 1], [5, 14, 2, 12], [9, 4, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [0, 8, 6, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 11, 13, 7], [8, 6, 0, 15]], [[10, 14, 3, 1], [5, 4, 2, 12], [9, 0, 13, 7], [8, 11, 6, 15]]], 'unique_positions': 17} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"6",
"3",
"5",
"1"
] | 1 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 0, 0], [1, 2, 1], [0, 0, 0]], 'minute_1': [[0, 0, 0], [2, 2, 2], [0, 0, 0]]}} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Two balls are dropped in sequence through the following holes: left, left. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many yellow faces can be seen in the middle row now? | [
"0",
"1",
"8",
"6"
] | 1 | {'start_state': [['yellow', 'blue', 'yellow'], ['blue', 'blue'], ['yellow', 'blue', 'yellow']], 'moves': ['left', 'left'], 'state_after_moves': [[['blue', 'blue', 'yellow'], ['blue', 'blue'], ['blue', 'blue', 'yellow']], [['yellow', 'blue', 'yellow'], ['yellow', 'blue'], ['yellow', 'blue', 'yellow']]], 'final_state': [['yellow', 'blue', 'yellow'], ['yellow', 'blue'], ['yellow', 'blue', 'yellow']]} |
|
The image shows the calendar of a month of a particular non-leap year. Which day of the week was on January 10 of that year? | [
"Sunday",
"Wednesday",
"Thursday",
"Friday"
] | Wednesday | {'image_year': 2525, 'image_month': [4, 'April'], 'query_year': 2525, 'query_month': [1, 'January'], 'query_day': 10} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Two balls are dropped in sequence through the following holes: right, right. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many yellow faces can be seen in the middle row now? | [
"8",
"5",
"0",
"1"
] | 1 | {'start_state': [['yellow', 'yellow', 'yellow'], ['yellow', 'yellow'], ['yellow', 'yellow', 'yellow']], 'moves': ['right', 'right'], 'state_after_moves': [[['yellow', 'yellow', 'blue'], ['yellow', 'blue'], ['yellow', 'yellow', 'blue']], [['yellow', 'yellow', 'yellow'], ['yellow', 'blue'], ['yellow', 'yellow', 'yellow']]], 'final_state': [['yellow', 'yellow', 'yellow'], ['yellow', 'blue'], ['yellow', 'yellow', 'yellow']]} |
|
A 3 * 3 Rubik's Cube has six different coloured panels: red, green, blue, yellow, orange, and grey. The initial state of the cube in terms of the different colour positions in its six faces is shown in the image. To represent the movements of the cube we use six letters: U for Up, D for Down, L for Left, R for Right, F for Front, B for Back. These letters are used in sequence where you need to perform each letter in the sequence from left to right. Each letter tells you to move that face clockwise by 90 degrees. A number 'n' immediately after a letter denotes that you need to move that face clockwise by 90 * n degrees. For example, 'U R3' would mean rotating the up face 90 degrees clockwise and then rotating the right face 270 degrees clockwise. You perform the move sequence 'U2 F3' starting from the state shown in the image. What would be the number of small 1 * 1 blue squares in the right face after completing the move sequence? | [
"0",
"2",
"4",
"5"
] | 2 | {'moves': 'U2 F3', 'query_face': 'right', 'query_colour': 'blue', 'start_position': {'left': [['red', 'grey', 'orange'], ['yellow', 'blue', 'red'], ['blue', 'green', 'grey']], 'right': [['green', 'grey', 'blue'], ['blue', 'green', 'yellow'], ['orange', 'blue', 'yellow']], 'down': [['yellow', 'red', 'blue'], ['orange', 'orange', 'red'], ['grey', 'orange', 'orange']], 'up': [['blue', 'green', 'orange'], ['green', 'grey', 'yellow'], ['green', 'orange', 'red']], 'back': [['red', 'red', 'grey'], ['green', 'red', 'blue'], ['green', 'blue', 'yellow']], 'front': [['red', 'yellow', 'grey'], ['orange', 'yellow', 'grey'], ['green', 'grey', 'yellow']]}, 'end_position': {'left': [['green', 'grey', 'blue'], ['yellow', 'blue', 'green'], ['blue', 'green', 'orange']], 'right': [['blue', 'grey', 'orange'], ['red', 'green', 'yellow'], ['yellow', 'blue', 'yellow']], 'down': [['blue', 'red', 'grey'], ['orange', 'orange', 'red'], ['grey', 'orange', 'orange']], 'up': [['red', 'orange', 'green'], ['yellow', 'grey', 'green'], ['red', 'blue', 'orange']], 'back': [['red', 'yellow', 'grey'], ['green', 'red', 'blue'], ['green', 'blue', 'yellow']], 'front': [['grey', 'grey', 'yellow'], ['red', 'yellow', 'grey'], ['red', 'orange', 'green']]}} |
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You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"4",
"2",
"3",
"5"
] | 2 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 1, 0], [2, 1, 0], [0, 0, 0]], 'minute_1': [[0, 1, 0], [2, 2, 0], [0, 0, 0]], 'minute_2': [[0, 2, 0], [2, 2, 0], [0, 0, 0]]}} |
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The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No. | [
"Yes",
"No"
] | No | {'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[0, 2], [2, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24} |
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You are given an incomplete map of a country having 15 different regions. The objective is to colour the regions of the map using only the four available colours: red, green, blue and yellow, such that no two adjacent regions have the same colour. Adjacent regions are defined as two regions that share a common boundary of non-zero length. The regions indicated by numbers 1 to 12 have already been coloured, as shown in the image. The regions indicated by numbers 13 to 15 are shown in white as they are yet to be coloured. You need to assign colours to these regions in a way such that it doesn't violate the objective. Each unique colour combination of the regions would result in a unique complete map. How many unique complete maps can be created by colouring all the white regions starting from the given incomplete map? | [
"4",
"2",
"1",
"3"
] | 4 | {'polygon_vertices': {'1': [[0.28309, 0.53419], [0.11076, 1.0], [0.0, 1.0], [0.0, 0.42264], [0.24203, 0.50918], [0.2808, 0.52947]], '2': [[0.81655, 0.98995], [0.82695, 0.87051], [0.92988, 0.74109], [1.0, 0.75424], [1.0, 0.90131]], '3': [[0.61832, 0.64358], [0.81645, 0.41358], [0.8425, 0.66388], [0.69657, 0.74761]], '4': [[0.50445, 1.0], [0.67229, 0.84031], [0.75972, 1.0]], '5': [[0.34158, 0.60012], [0.42827, 0.8191], [0.67368, 0.78375], [0.69382, 0.75855], [0.69657, 0.74761], [0.61832, 0.64358]], '6': [[0.11076, 1.0], [0.4312, 1.0], [0.42827, 0.8191], [0.34158, 0.60012], [0.28309, 0.53419]], '7': [[0.84357, 0.26097], [0.81645, 0.41358], [0.8425, 0.66388], [0.92988, 0.74109], [1.0, 0.75424], [1.0, 0.12583]], '8': [[0.84357, 0.26097], [0.81645, 0.41358], [0.61832, 0.64358], [0.34158, 0.60012], [0.28309, 0.53419], [0.2808, 0.52947], [0.61289, 0.31]], '9': [[0.2808, 0.52947], [0.61289, 0.31], [0.39095, 0.09208], [0.24203, 0.50918]], '10': [[0.81655, 0.98995], [0.81089, 1.0], [0.75972, 1.0], [0.67229, 0.84031], [0.67368, 0.78375], [0.69382, 0.75855], [0.82695, 0.87051]], '11': [[0.50445, 1.0], [0.4312, 1.0], [0.42827, 0.8191], [0.67368, 0.78375], [0.67229, 0.84031]], '12': [[0.69657, 0.74761], [0.69382, 0.75855], [0.82695, 0.87051], [0.92988, 0.74109], [0.8425, 0.66388]], '13': [[0.34958, 0.0], [0.39095, 0.09208], [0.61289, 0.31], [0.84357, 0.26097], [1.0, 0.12583], [1.0, 0.0]], '14': [[1.0, 1.0], [1.0, 0.90131], [0.81655, 0.98995], [0.81089, 1.0]], '15': [[0.39095, 0.09208], [0.24203, 0.50918], [0.0, 0.42264], [0.0, 0.0], [0.34958, 0.0]]}, 'polygon_adjacency_list': [[1, 6], [1, 8], [1, 9], [1, 15], [2, 7], [2, 10], [2, 12], [2, 14], [3, 5], [3, 7], [3, 8], [3, 12], [4, 10], [4, 11], [5, 3], [5, 6], [5, 8], [5, 10], [5, 11], [5, 12], [6, 1], [6, 5], [6, 8], [6, 11], [7, 2], [7, 3], [7, 8], [7, 12], [7, 13], [8, 1], [8, 3], [8, 5], [8, 6], [8, 7], [8, 9], [8, 13], [9, 1], [9, 8], [9, 13], [9, 15], [10, 2], [10, 4], [10, 5], [10, 11], [10, 12], [10, 14], [11, 4], [11, 5], [11, 6], [11, 10], [12, 2], [12, 3], [12, 5], [12, 7], [12, 10], [13, 7], [13, 8], [13, 9], [13, 15], [14, 2], [14, 10], [15, 1], [15, 9], [15, 13]], 'known_colours': {'1': 'Red', '2': 'Green', '3': 'Blue', '4': 'Red', '5': 'Yellow', '6': 'Blue', '7': 'Yellow', '8': 'Green', '9': 'Blue', '10': 'Blue', '11': 'Green', '12': 'Red'}, 'possible_colours_of_unknown': [{'13': 'Red', '14': 'Yellow', '15': 'Green'}, {'13': 'Red', '14': 'Yellow', '15': 'Yellow'}, {'13': 'Red', '14': 'Red', '15': 'Green'}, {'13': 'Red', '14': 'Red', '15': 'Yellow'}], 'unique_maps': 4, 'total_regions': 15, 'known_regions': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'unknown_regions': [13, 14, 15]} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"6",
"1",
"3",
"4"
] | 6 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 1, 1], [1, 0, 2], [1, 1, 0]], 'minute_1': [[1, 1, 2], [1, 0, 2], [1, 1, 0]], 'minute_2': [[1, 2, 2], [1, 0, 2], [1, 1, 0]], 'minute_3': [[2, 2, 2], [1, 0, 2], [1, 1, 0]], 'minute_4': [[2, 2, 2], [2, 0, 2], [1, 1, 0]], 'minute_5': [[2, 2, 2], [2, 0, 2], [2, 1, 0]], 'minute_6': [[2, 2, 2], [2, 0, 2], [2, 2, 0]]}} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"3",
"2",
"1",
"6"
] | 2 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 2, 1], [1, 1, 1], [0, 1, 0]], 'minute_1': [[0, 2, 2], [1, 2, 1], [0, 1, 0]], 'minute_2': [[0, 2, 2], [2, 2, 2], [0, 2, 0]]}} |
|
You are playing a Tower of Hanoi game with 3 rods and 5 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"3",
"1",
"6",
"2"
] | 2 | {'start_position': [[3], [2], [5, 4, 1]], 'end_position': [[3, 2, 1], [], [5, 4]], 'moves': [{'position': [[3], [2], [5, 4, 1]], 'num_moves': 0}, {'position': [[3, 2], [], [5, 4, 1]], 'num_moves': 1}, {'position': [[3, 2, 1], [], [5, 4]], 'num_moves': 2}]} |
|
Consider a sliding block puzzle of grid size 5 * 4 units. It has 9 wooden blocks of varying sizes: one 2 * 2, four 1 * 2, two 2 * 1, and two 1 * 1. The gird also has two empty 1 * 1 spaces. The blocks cannot be removed from the grid, and may only be slid horizontally and vertically within its boundary. A move is defined as selecting a block that is slideable, and moving it by 1 unit either horizontally or vertically, whichever is possible. The image shows the starting and ending configurations of the puzzle grid. The wooden blocks are shown in various shades of brown and the empty spaces are shown in white. What is the minimum number of moves required to reach the ending configuration from the starting configuration? | [
"6",
"4",
"3",
"5"
] | 5 | {'start_position': '2233\n6114\n6115\n7880\n7099', 'end_position': '2233\n1104\n1105\n6788\n6799', 'moves': ['2233\n6114\n6115\n7880\n7099', '2233\n6114\n6115\n7088\n7099', '2233\n6114\n6115\n0788\n0799', '2233\n0114\n6115\n6788\n0799', '2233\n0114\n0115\n6788\n6799', '2233\n1104\n1105\n6788\n6799']} |
|
A checker game is being played on a grid of 8 squares with 5 green and 2 red checkers. Initially, the checkers are arranged as shown in the starting configuration with the 7 checkers occupying 7 squares and one unoccupied square. Green checkers only move rightward and red checkers only move leftward. Every move is either i) a slide to the adjacent empty square, or ii) a jump over one position to an empty square, provided the checker being jumped over is of a different colour. Each square can accommodate a maximum of one checker at any time. How many moves are required to reach the ending configuration from the starting configuration following the specified rules? | [
"1",
"5",
"2",
"4"
] | 1 | {'start_position': 'GGRG_GRG', 'end_position': 'GGRGRG_G', 'green_checkers': 5, 'red_checkers': 2, 'moves': ['GGRG_GRG', 'GGRGRG_G']} |
|
A checker game is being played on a grid of 7 squares with 4 green and 2 red checkers. Initially, the checkers are arranged as shown in the starting configuration with the 6 checkers occupying 6 squares and one unoccupied square. Green checkers only move rightward and red checkers only move leftward. Every move is either i) a slide to the adjacent empty square, or ii) a jump over one position to an empty square, provided the checker being jumped over is of a different colour. Each square can accommodate a maximum of one checker at any time. How many moves are required to reach the ending configuration from the starting configuration following the specified rules? | [
"41",
"32",
"14",
"38"
] | 14 | {'start_position': 'GGGG_RR', 'end_position': 'RR_GGGG', 'green_checkers': 4, 'red_checkers': 2, 'moves': ['GGGG_RR', 'GGG_GRR', 'GGGRG_R', 'GGGRGR_', 'GGGR_RG', 'GG_RGRG', 'G_GRGRG', 'GRG_GRG', 'GRGRG_G', 'GRGR_GG', 'GR_RGGG', '_RGRGGG', 'R_GRGGG', 'RRG_GGG', 'RR_GGGG']} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"1",
"4",
"2",
"6"
] | 1 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 2, 1], [0, 1, 0], [0, 0, 0]], 'minute_1': [[2, 2, 2], [0, 2, 0], [0, 0, 0]]}} |
|
This is maze having 9 * 13 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. How many cells do you need to visit in this optimal path including the entrance and exit cells? | [
"42",
"24",
"35",
"27"
] | 27 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [1, 2], [1, 3], [2, 3], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [7, 2], [7, 3], [6, 3], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [6, 11], [7, 11], [8, 11]], 'optimal_path_length': 27, 'left_turns': 3, 'right_turns': 4, 'total_turns': 7} |
|
Alice has 14 segments of chains of different lengths as shown in the image. The total length of all the segments combined is 39 pieces. She has a saw machine with which a closed piece can be cut opened. She also has a welding machine with which an open piece can be closed. Each cut takes 3 minutes and each welding takes 2 minutes. Initially, she has 2 segments each with 1 open piece as shown in the image. All the other pieces are closed. She now wants to make the longest possible necklace using all the available 39 pieces. Each piece in the necklace would be connected to exactly two other pieces. This would require cutting open some pieces and then joining all the resulting segments together. What is the minimum time in which she can create the necklace? | [
"25",
"30",
"39",
"4"
] | 39 | {'steps': [[2, 1, 3, 4, 2, 2], [3, 0, 3, 4, 2, 2], [4, 1, 2, 4, 2, 2], [5, 0, 2, 4, 2, 2], [6, 1, 1, 4, 2, 2], [7, 0, 1, 4, 2, 2], [8, 1, 0, 4, 2, 2], [9, 0, 0, 4, 2, 2]], 'cuts': 7, 'joins': 9, 'each_cut_time': 3, 'each_join_time': 2, 'total_time': 39} |
|
A storekeeper is a puzzle in which the player pushes boxes around in a warehouse trying to get them to target locations. The game is represented by an 6 x 6 grid of characters grid where each element is a wall, floor, or box. Your task is to move the box to the end flag under the following rules:
1. The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box by 1 grid. This is a push.
2. The player cannot walk through the box.
What is the minimum number of pushes to move the box to the end flag. | [
"3",
"1",
"4",
"2"
] | 4 | {'ids': {'empty': '.', 'brick': '#', 'box': 'B', 'person': 'S', 'target': 'T'}, 'timestep': {'grid_0': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '.', '.', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '.', 'B', 'S', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_1': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '.', '.', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', 'B', 'S', '', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_2': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '.', '.', '#'], ['#', '.', 'B', '.', '#', '#'], ['#', '#', 'S', '', '', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_3': [['#', '#', '#', '#', '#', '#'], ['#', 'T', 'B', '.', '.', '#'], ['#', '.', 'S', '.', '#', '#'], ['#', '#', '.', '', '', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_4': [['#', '#', '#', '#', '#', '#'], ['#', 'B', 'S', '.', '.', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '.', '', '', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '#', '#', '#', '#', '#']]}, 'target': [1, 1], 'box_location': [[3, 3], [3, 2], [2, 2], [1, 2], [1, 1]]} |
|
Alice has 14 segments of chains of different lengths as shown in the image. The total length of all the segments combined is 30 pieces. She has a saw machine with which a closed piece can be cut opened. She also has a welding machine with which an open piece can be closed. Each cut takes 5 minutes and each welding takes 5 minutes. Initially, she has 4 segments each with 1 open piece as shown in the image. All the other pieces are closed. She now wants to make the longest possible necklace using all the available 30 pieces. Each piece in the necklace would be connected to exactly two other pieces. This would require cutting open some pieces and then joining all the resulting segments together. What is the minimum time in which she can create the necklace? | [
"60",
"14",
"13",
"54"
] | 60 | {'steps': [[4, 2, 2, 4, 2, 0], [5, 1, 2, 4, 2, 0], [6, 0, 2, 4, 2, 0], [7, 1, 1, 4, 2, 0], [8, 0, 1, 4, 2, 0]], 'cuts': 4, 'joins': 8, 'each_cut_time': 5, 'each_join_time': 5, 'total_time': 60} |
|
A storekeeper is a puzzle in which the player pushes boxes around in a warehouse trying to get them to target locations. The game is represented by an 6 x 6 grid of characters grid where each element is a wall, floor, or box. Your task is to move the box to the end flag under the following rules:
1. The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box by 1 grid. This is a push.
2. The player cannot walk through the box.
What is the minimum number of pushes to move the box to the end flag. | [
"4",
"2",
"5",
"1"
] | 4 | {'ids': {'empty': '.', 'brick': '#', 'box': 'B', 'person': 'S', 'target': 'T'}, 'timestep': {'grid_0': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '#', '#', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '.', '.', 'B', 'S', '#'], ['#', '.', '.', '#', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_1': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '#', '#', '#'], ['#', '.', '.', '.', '#', '#'], ['#', '.', 'B', 'S', '', '#'], ['#', '.', '.', '#', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_2': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '#', '#', '#'], ['#', '.', 'B', '.', '#', '#'], ['#', '.', 'S', '', '', '#'], ['#', '.', '.', '#', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_3': [['#', '#', '#', '#', '#', '#'], ['#', 'T', '.', '#', '#', '#'], ['#', 'B', 'S', '.', '#', '#'], ['#', '.', '.', '', '', '#'], ['#', '.', '.', '#', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_4': [['#', '#', '#', '#', '#', '#'], ['#', 'B', '.', '#', '#', '#'], ['#', 'S', '.', '.', '#', '#'], ['#', '.', '.', '', '', '#'], ['#', '.', '.', '#', '.', '#'], ['#', '#', '#', '#', '#', '#']]}, 'target': [1, 1], 'box_location': [[3, 3], [3, 2], [2, 2], [2, 1], [1, 1]]} |
|
The board shown in the image is a sliding puzzle of 5 * 5 tile dimensions. It has 24 numbered tiles and one unoccupied (open) position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. All tiles always stay and move inside the red boundary wall, as shown in the image. A move is defined as moving the open position by one tile unit in any available direction. You start from the board position shown in the image and perform exactly 3 moves. How many unique final board positions can you reach? | [
"13",
"12",
"24",
"1"
] | 12 | {'starting_grid': [[10, 12, 22, 24, 0], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'total_moves': 3, 'path_track': {'left, left, left': [[10, 0, 12, 22, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, left, right': [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, left, down': [[10, 12, 7, 22, 24], [15, 21, 0, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, right, left': [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, right, down': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, down, left': [[10, 12, 22, 17, 24], [15, 21, 0, 7, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, down, right': [[10, 12, 22, 17, 24], [15, 21, 7, 4, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, down, up': [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'left, down, down': [[10, 12, 22, 17, 24], [15, 21, 7, 1, 4], [19, 6, 18, 0, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, left, left': [[10, 12, 22, 24, 4], [15, 21, 0, 7, 17], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, left, right': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, left, up': [[10, 12, 22, 0, 4], [15, 21, 7, 24, 17], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, left, down': [[10, 12, 22, 24, 4], [15, 21, 7, 1, 17], [19, 6, 18, 0, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, up, left': [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, up, down': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, down, left': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 2], [19, 6, 18, 0, 1], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, down, up': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], 'down, down, down': [[10, 12, 22, 24, 4], [15, 21, 7, 17, 2], [19, 6, 18, 1, 11], [5, 20, 13, 8, 0], [16, 14, 23, 9, 3]]}, 'possible_states': [[[10, 0, 12, 22, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 7, 22, 24], [15, 21, 0, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 17, 24], [15, 21, 0, 7, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 17, 24], [15, 21, 7, 4, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 17, 24], [15, 21, 7, 1, 4], [19, 6, 18, 0, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 0, 7, 17], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 0, 4], [15, 21, 7, 24, 17], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 1, 17], [19, 6, 18, 0, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 0, 24], [15, 21, 7, 17, 4], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 2], [19, 6, 18, 0, 1], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 0], [19, 6, 18, 1, 2], [5, 20, 13, 8, 11], [16, 14, 23, 9, 3]], [[10, 12, 22, 24, 4], [15, 21, 7, 17, 2], [19, 6, 18, 1, 11], [5, 20, 13, 8, 0], [16, 14, 23, 9, 3]]], 'unique_positions': 12} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"3",
"4",
"6",
"1"
] | 4 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 1, 2], [1, 1, 1], [1, 0, 0]], 'minute_1': [[1, 2, 2], [1, 1, 2], [1, 0, 0]], 'minute_2': [[2, 2, 2], [1, 2, 2], [1, 0, 0]], 'minute_3': [[2, 2, 2], [2, 2, 2], [1, 0, 0]], 'minute_4': [[2, 2, 2], [2, 2, 2], [2, 0, 0]]}} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Three balls are dropped in sequence through the following holes: right, center, center. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many yellow faces can be seen in total in all the rows now? | [
"5",
"8",
"6",
"2"
] | 5 | {'start_state': [['yellow', 'yellow', 'yellow'], ['yellow', 'yellow'], ['yellow', 'yellow', 'yellow']], 'moves': ['right', 'center', 'center'], 'state_after_moves': [[['yellow', 'yellow', 'blue'], ['yellow', 'blue'], ['yellow', 'yellow', 'blue']], [['yellow', 'blue', 'blue'], ['yellow', 'yellow'], ['yellow', 'blue', 'blue']], [['yellow', 'yellow', 'blue'], ['blue', 'yellow'], ['yellow', 'yellow', 'blue']]], 'final_state': [['yellow', 'yellow', 'blue'], ['blue', 'yellow'], ['yellow', 'yellow', 'blue']]} |
|
Nicholas's event is going to start in 1 hour 13 minutes. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What will be the time when the event starts? | [
"2:32",
"6:39",
"0:37",
"1:47"
] | 0:37 | {'current_hour': 11, 'current_minute': 24, 'add_hour': 1, 'add_minute': 13} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Three balls are dropped in sequence through the following holes: left, center, center. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many blue faces can be seen in the top row now? | [
"3",
"7",
"1",
"2"
] | 2 | {'start_state': [['blue', 'blue', 'blue'], ['blue', 'blue'], ['blue', 'blue', 'blue']], 'moves': ['left', 'center', 'center'], 'state_after_moves': [[['yellow', 'blue', 'blue'], ['yellow', 'blue'], ['yellow', 'blue', 'blue']], [['yellow', 'yellow', 'blue'], ['blue', 'blue'], ['yellow', 'yellow', 'blue']], [['yellow', 'blue', 'blue'], ['blue', 'yellow'], ['yellow', 'blue', 'blue']]], 'final_state': [['yellow', 'blue', 'blue'], ['blue', 'yellow'], ['yellow', 'blue', 'blue']]} |
|
A 5 * 5 board consists of 25 different coloured tiles. A random state of the board is shown in (A). The ideal state of the board is shown in (B). A swap consists of selecting any two tiles on the board and switching their positions. What is the minimum number of swaps required to restore the ideal state of the board from (A)? | [
"2",
"5",
"9",
"7"
] | 7 | {'ideal_grid': [[[255, 111, 60], [255, 133, 60], [255, 155, 60], [255, 177, 60], [255, 201, 60]], [[207, 122, 95], [207, 144, 89], [207, 167, 84], [207, 190, 78], [207, 214, 72]], [[159, 133, 130], [159, 155, 118], [159, 179, 108], [159, 203, 96], [159, 227, 84]], [[111, 144, 165], [111, 166, 147], [111, 191, 132], [111, 216, 114], [111, 240, 96]], [[60, 155, 201], [60, 180, 179], [60, 205, 157], [60, 230, 135], [60, 255, 111]]], 'shuffled_grid': [[[255, 133, 60], [111, 191, 132], [255, 155, 60], [159, 179, 108], [207, 122, 95]], [[207, 214, 72], [207, 144, 89], [207, 167, 84], [207, 190, 78], [255, 111, 60]], [[159, 133, 130], [159, 155, 118], [255, 201, 60], [159, 203, 96], [159, 227, 84]], [[111, 144, 165], [111, 166, 147], [255, 177, 60], [111, 216, 114], [111, 240, 96]], [[60, 155, 201], [60, 180, 179], [60, 205, 157], [60, 230, 135], [60, 255, 111]]], 'shuffled_order': [1, 17, 2, 12, 5, 9, 6, 7, 8, 0, 10, 11, 4, 13, 14, 15, 16, 3, 18, 19, 20, 21, 22, 23, 24], 'swaps': 7, 'in_position': 17, 'out_of_position': 8} |
|
This is maze having 13 * 13 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. How many cells do you need to visit in this optimal path including the entrance and exit cells? | [
"27",
"43",
"47",
"31"
] | 27 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 7], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 11], [5, 11], [5, 10], [5, 9], [6, 9], [7, 9], [7, 10], [7, 11], [8, 11], [9, 11], [10, 11], [11, 11], [12, 11]], 'optimal_path_length': 27, 'left_turns': 3, 'right_turns': 4, 'total_turns': 7} |
|
Consider a sliding block puzzle of grid size 5 * 4 units. It has 9 wooden blocks of varying sizes: one 2 * 2, four 1 * 2, two 2 * 1, and two 1 * 1. The gird also has two empty 1 * 1 spaces. The blocks cannot be removed from the grid, and may only be slid horizontally and vertically within its boundary. A move is defined as selecting a block that is slideable, and moving it by 1 unit either horizontally or vertically, whichever is possible. The image shows the starting and ending configurations of the puzzle grid. The wooden blocks are shown in various shades of brown and the empty spaces are shown in white. What is the minimum number of moves required to reach the ending configuration from the starting configuration? | [
"4",
"2",
"5",
"6"
] | 5 | {'start_position': '2233\n6110\n6114\n7880\n7995', 'end_position': '2233\n6114\n6115\n7088\n7099', 'moves': ['2233\n6110\n6114\n7880\n7995', '2233\n6110\n6114\n7885\n7990', '2233\n6110\n6114\n7885\n7099', '2233\n6114\n6110\n7885\n7099', '2233\n6114\n6115\n7880\n7099', '2233\n6114\n6115\n7088\n7099']} |
|
The image shows the calendar of a month of a particular non-leap year. The next year was a non-leap year. Which day of the week was on July 26 of the next year? | [
"Saturday",
"Thursday",
"Friday",
"Monday"
] | Thursday | {'image_year': 1922, 'image_month': [5, 'May'], 'query_year': 1923, 'query_month': [7, 'July'], 'query_day': 26} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"4",
"3",
"1",
"6"
] | 4 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 1, 0], [2, 0, 1], [1, 1, 1]], 'minute_1': [[2, 1, 0], [2, 0, 1], [2, 1, 1]], 'minute_2': [[2, 2, 0], [2, 0, 1], [2, 2, 1]], 'minute_3': [[2, 2, 0], [2, 0, 1], [2, 2, 2]], 'minute_4': [[2, 2, 0], [2, 0, 2], [2, 2, 2]]}} |
|
Sarah's event is going to start in 53 minutes. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What will be the time when the event starts? | [
"8:18",
"4:26",
"3:15",
"5:17"
] | 3:15 | {'current_hour': 2, 'current_minute': 22, 'add_hour': 0, 'add_minute': 53} |
|
The checkerboard shown in the image was originally of 8 * 7 in dimension having a total of 56 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 27 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 27 dominoes in the checkerboard to exactly cover all the remaining 54 squares? Answer Yes or No. | [
"No",
"Yes"
] | No | {'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 7, 'removed_positions': [[1, 2], [3, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 28, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26} |
|
You are given a 9 * 9 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 9 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 7 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"5",
"4",
"8",
"6"
] | 4 | {'rows': 9, 'columns': 9, 'given_queen_positions': [[0, 2], [1, 4], [2, 6], [5, 1], [6, 7], [7, 5], [8, 8]], 'missing_queen_positions': [[3, 0], [4, 3]]} |
|
Consider a sliding block puzzle of grid size 5 * 4 units. It has 9 wooden blocks of varying sizes: one 2 * 2, four 1 * 2, two 2 * 1, and two 1 * 1. The gird also has two empty 1 * 1 spaces. The blocks cannot be removed from the grid, and may only be slid horizontally and vertically within its boundary. A move is defined as selecting a block that is slideable, and moving it by 1 unit either horizontally or vertically, whichever is possible. The image shows the starting and ending configurations of the puzzle grid. The wooden blocks are shown in various shades of brown and the empty spaces are shown in white. What is the minimum number of moves required to reach the ending configuration from the starting configuration? | [
"1",
"5",
"6",
"2"
] | 2 | {'start_position': '1122\n1133\n0405\n6788\n6799', 'end_position': '1122\n1133\n4050\n6788\n6799', 'moves': ['1122\n1133\n0405\n6788\n6799', '1122\n1133\n0450\n6788\n6799', '1122\n1133\n4050\n6788\n6799']} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Two balls are dropped in sequence through the following holes: right, center. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many blue faces can be seen in the middle row now? | [
"5",
"4",
"1",
"2"
] | 1 | {'start_state': [['blue', 'yellow', 'blue'], ['yellow', 'yellow'], ['blue', 'yellow', 'blue']], 'moves': ['right', 'center'], 'state_after_moves': [[['blue', 'yellow', 'yellow'], ['yellow', 'yellow'], ['blue', 'yellow', 'yellow']], [['blue', 'blue', 'yellow'], ['yellow', 'blue'], ['blue', 'yellow', 'blue']]], 'final_state': [['blue', 'blue', 'yellow'], ['yellow', 'blue'], ['blue', 'yellow', 'blue']]} |
|
The checkerboard shown in the image was originally of 7 * 9 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No. | [
"Yes",
"No"
] | Yes | {'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 9, 'removed_positions': [[4, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 31, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 31} |
|
This is maze having 11 * 9 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of right turns do you need to make in this optimal path? | [
"5",
"2",
"1",
"3"
] | 5 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1]], 'optimal_path': [[1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [2, 5], [3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [7, 2], [7, 3], [8, 3], [9, 3], [9, 4], [9, 5], [8, 5], [7, 5], [7, 6], [7, 7], [8, 7], [9, 7], [9, 8]], 'optimal_path_length': 29, 'left_turns': 5, 'right_turns': 5, 'total_turns': 10} |
|
The image shows the calendar of a month of a particular non-leap year. The previous year was a non-leap year. Which day of the week was on June 12 of the previous year? | [
"Sunday",
"Wednesday",
"Thursday",
"Saturday"
] | Saturday | {'image_year': 2338, 'image_month': [11, 'November'], 'query_year': 2337, 'query_month': [6, 'June'], 'query_day': 12} |
|
You are given a 10 * 10 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 10 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 8 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"11",
"9",
"8",
"10"
] | 9 | {'rows': 10, 'columns': 10, 'given_queen_positions': [[1, 5], [2, 8], [3, 0], [4, 9], [5, 4], [6, 6], [7, 1], [9, 7]], 'missing_queen_positions': [[0, 2], [8, 3]]} |
|
The toy shown in the figure has eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face. When a ball passes through a disc it tips the disk mechanism which flips the face color. The tipping of the disc mechanism determines whether the ball would be deflected to the left or to the right. The vertical walls between the discs would then determine the path of motion of the ball. A dropped ball always passes through exactly one disc in each of the top and the bottom row. Depending on the configuration of the top three discs it may or may not pass through the middle row. Finally, when the ball falls to the bottom it would exit either to a hole on the left or the right of the device. Three balls are dropped in sequence through the following holes: left, left, left. Consider the toy configuration after all the balls have been dropped and they have exited from the bottom. How many blue faces can be seen in total in all the rows now? | [
"4",
"2",
"6",
"1"
] | 6 | {'start_state': [['blue', 'blue', 'blue'], ['blue', 'blue'], ['blue', 'blue', 'blue']], 'moves': ['left', 'left', 'left'], 'state_after_moves': [[['yellow', 'blue', 'blue'], ['yellow', 'blue'], ['yellow', 'blue', 'blue']], [['blue', 'blue', 'blue'], ['yellow', 'blue'], ['blue', 'blue', 'blue']], [['yellow', 'blue', 'blue'], ['blue', 'blue'], ['blue', 'yellow', 'blue']]], 'final_state': [['yellow', 'blue', 'blue'], ['blue', 'blue'], ['blue', 'yellow', 'blue']]} |
|
This is maze having 11 * 9 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of right turns do you need to make in this optimal path? | [
"1",
"2",
"4",
"5"
] | 5 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [4, 5], [3, 5], [3, 6], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [7, 5], [8, 5], [9, 5], [9, 6], [9, 7], [10, 7]], 'optimal_path_length': 25, 'left_turns': 4, 'right_turns': 5, 'total_turns': 9} |
|
Alice has 12 segments of chains of different lengths as shown in the image. The total length of all the segments combined is 30 pieces. She has a saw machine with which a closed piece can be cut opened. She also has a welding machine with which an open piece can be closed. Each cut takes 4 minutes and each welding takes 2 minutes. Initially, she has 4 segments each with 1 open piece as shown in the image. All the other pieces are closed. She now wants to make the longest possible necklace using all the available 30 pieces. Each piece in the necklace would be connected to exactly two other pieces. This would require cutting open some pieces and then joining all the resulting segments together. What is the minimum time in which she can create the necklace? | [
"21",
"33",
"3",
"26"
] | 26 | {'steps': [[4, 0, 1, 4, 3, 0], [5, 1, 0, 4, 3, 0], [6, 0, 0, 4, 3, 0], [7, 0, 1, 3, 3, 0]], 'cuts': 3, 'joins': 7, 'each_cut_time': 4, 'each_join_time': 2, 'total_time': 26} |
|
Hannah came to an event 3 hours 39 minutes ago. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What was the time when Hannah came to the event? | [
"2:47",
"10:56",
"9:16",
"10:37"
] | 10:56 | {'current_hour': 2, 'current_minute': 35, 'subtract_hour': 3, 'subtract_minute': 39} |
|
A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize? | [
"Money",
"Car",
"Vacation",
"Jewelry"
] | Money | {'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 315, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['silver', 'yellow', 'orangered', 'lime', 'cyan', 'darkorange', 'blanchedalmond', 'magenta'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Money', 'Camera', 'Jewelry', 'Car', 'Watch', 'Vacation', 'Chocolate'], 'rotated_colors': ['lime', 'cyan', 'darkorange', 'blanchedalmond', 'magenta', 'silver', 'yellow', 'orangered'], 'rotated_boundaries': [18.0, 63.0, 108.0, 153.0, 198.0, 243.0, 288.0, 333.0], 'rotated_prizes': ['Jewelry', 'Car', 'Watch', 'Vacation', 'Chocolate', 'Laptop', 'Money', 'Camera']} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"5",
"3",
"4",
"6"
] | 4 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 1, 0], [0, 1, 1], [2, 1, 0]], 'minute_1': [[1, 1, 0], [0, 1, 1], [2, 2, 0]], 'minute_2': [[1, 1, 0], [0, 2, 1], [2, 2, 0]], 'minute_3': [[1, 2, 0], [0, 2, 2], [2, 2, 0]], 'minute_4': [[2, 2, 0], [0, 2, 2], [2, 2, 0]]}} |
|
You are playing a Tower of Hanoi game with 3 rods and 5 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"2",
"5",
"6",
"1"
] | 1 | {'start_position': [[5, 4, 1], [], [3, 2]], 'end_position': [[5, 4, 1], [2], [3]], 'moves': [{'position': [[5, 4, 1], [], [3, 2]], 'num_moves': 0}, {'position': [[5, 4, 1], [2], [3]], 'num_moves': 1}]} |
|
You are playing a Tower of Hanoi game with 3 rods and 6 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"6",
"5",
"3",
"1"
] | 3 | {'start_position': [[4, 1], [3, 2], [6, 5]], 'end_position': [[4, 3], [], [6, 5, 2, 1]], 'moves': [{'position': [[4, 1], [3, 2], [6, 5]], 'num_moves': 0}, {'position': [[4, 1], [3], [6, 5, 2]], 'num_moves': 1}, {'position': [[4], [3], [6, 5, 2, 1]], 'num_moves': 2}, {'position': [[4, 3], [], [6, 5, 2, 1]], 'num_moves': 3}]} |
|
You are playing a Tower of Hanoi game with 3 rods and 4 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"5",
"6",
"2",
"4"
] | 5 | {'start_position': [[4, 3], [], [2, 1]], 'end_position': [[], [3, 2, 1], [4]], 'moves': [{'position': [[4, 3], [], [2, 1]], 'num_moves': 0}, {'position': [[4], [3], [2, 1]], 'num_moves': 1}, {'position': [[4, 1], [3], [2]], 'num_moves': 2}, {'position': [[4, 1], [3, 2], []], 'num_moves': 3}, {'position': [[4], [3, 2, 1], []], 'num_moves': 4}, {'position': [[], [3, 2, 1], [4]], 'num_moves': 5}]} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"5",
"4",
"3",
"6"
] | 4 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 1, 1], [1, 1, 0], [2, 1, 0]], 'minute_1': [[1, 1, 1], [2, 1, 0], [2, 2, 0]], 'minute_2': [[2, 1, 1], [2, 2, 0], [2, 2, 0]], 'minute_3': [[2, 2, 1], [2, 2, 0], [2, 2, 0]], 'minute_4': [[2, 2, 2], [2, 2, 0], [2, 2, 0]]}} |
|
Elizabeth's event is going to start in 2 hours 39 minutes. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What will be the time when the event starts? | [
"9:27",
"10:02",
"6:09",
"3:47"
] | 10:02 | {'current_hour': 7, 'current_minute': 23, 'add_hour': 2, 'add_minute': 39} |
|
A checker game is being played on a grid of 8 squares with 4 green and 3 red checkers. Initially, the checkers are arranged as shown in the starting configuration with the 7 checkers occupying 7 squares and one unoccupied square. Green checkers only move rightward and red checkers only move leftward. Every move is either i) a slide to the adjacent empty square, or ii) a jump over one position to an empty square, provided the checker being jumped over is of a different colour. Each square can accommodate a maximum of one checker at any time. How many moves are required to reach the ending configuration from the starting configuration following the specified rules? | [
"1",
"0",
"4",
"3"
] | 3 | {'start_position': 'G_GRGRGR', 'end_position': 'GRGRGRG_', 'green_checkers': 4, 'red_checkers': 3, 'moves': ['G_GRGRGR', 'GRG_GRGR', 'GRGRG_GR', 'GRGRGRG_']} |
|
You are given an incomplete map of a country having 19 different regions. The objective is to colour the regions of the map using only the four available colours: red, green, blue and yellow, such that no two adjacent regions have the same colour. Adjacent regions are defined as two regions that share a common boundary of non-zero length. The regions indicated by numbers 1 to 14 have already been coloured, as shown in the image. The regions indicated by numbers 15 to 19 are shown in white as they are yet to be coloured. You need to assign colours to these regions in a way such that it doesn't violate the objective. Each unique colour combination of the regions would result in a unique complete map. How many unique complete maps can be created by colouring all the white regions starting from the given incomplete map? | [
"7",
"4",
"5",
"9"
] | 4 | {'polygon_vertices': {'1': [[0.41219, 0.40897], [0.36574, 0.41999], [0.14233, 0.61547], [0.25075, 0.7056], [0.46405, 0.5481], [0.44037, 0.45036]], '2': [[0.86585, 0.67186], [1.0, 0.5651], [1.0, 0.84986], [0.85795, 0.77639]], '3': [[1.0, 0.42319], [0.95952, 0.39986], [0.71543, 0.18907], [0.69832, 0.1478], [0.75664, 0.0], [1.0, 0.0]], '4': [[0.14233, 0.61547], [0.36574, 0.41999], [0.23948, 0.43007], [0.05677, 0.56473]], '5': [[0.57727, 1.0], [0.61079, 0.71792], [0.57244, 0.62873], [0.46405, 0.5481], [0.25075, 0.7056], [0.26317, 1.0]], '6': [[0.1046, 0.39364], [0.0, 0.27796], [0.0, 0.56599], [0.04208, 0.56118]], '7': [[0.23948, 0.43007], [0.05677, 0.56473], [0.04208, 0.56118], [0.1046, 0.39364], [0.15459, 0.339]], '8': [[0.79277, 1.0], [0.85795, 0.77639], [1.0, 0.84986], [1.0, 1.0]], '9': [[0.15932, 0.31619], [0.15459, 0.339], [0.23948, 0.43007], [0.36574, 0.41999], [0.41219, 0.40897], [0.39157, 0.21637], [0.35649, 0.18401]], '10': [[0.95952, 0.39986], [0.6932, 0.41791], [0.68631, 0.52896], [1.0, 0.50414], [1.0, 0.42319]], '11': [[0.0, 1.0], [0.0, 0.56599], [0.04208, 0.56118], [0.05677, 0.56473], [0.14233, 0.61547], [0.25075, 0.7056], [0.26317, 1.0]], '12': [[0.6576, 0.36575], [0.71543, 0.18907], [0.95952, 0.39986], [0.6932, 0.41791]], '13': [[0.1046, 0.39364], [0.15459, 0.339], [0.15932, 0.31619], [0.0, 0.20635], [0.0, 0.27796]], '14': [[0.69832, 0.1478], [0.71543, 0.18907], [0.6576, 0.36575], [0.44037, 0.45036], [0.41219, 0.40897], [0.39157, 0.21637]], '15': [[0.0, 0.20635], [0.15932, 0.31619], [0.35649, 0.18401], [0.25937, 0.0], [0.0, 0.0]], '16': [[0.86585, 0.67186], [0.61079, 0.71792], [0.57727, 1.0], [0.79277, 1.0], [0.85795, 0.77639]], '17': [[0.35649, 0.18401], [0.39157, 0.21637], [0.69832, 0.1478], [0.75664, 0.0], [0.25937, 0.0]], '18': [[0.68631, 0.52896], [0.6932, 0.41791], [0.6576, 0.36575], [0.44037, 0.45036], [0.46405, 0.5481], [0.57244, 0.62873]], '19': [[1.0, 0.50414], [0.68631, 0.52896], [0.57244, 0.62873], [0.61079, 0.71792], [0.86585, 0.67186], [1.0, 0.5651]]}, 'polygon_adjacency_list': [[1, 4], [1, 5], [1, 9], [1, 11], [1, 14], [1, 18], [2, 8], [2, 16], [2, 19], [3, 10], [3, 12], [3, 14], [3, 17], [4, 1], [4, 7], [4, 9], [4, 11], [5, 1], [5, 11], [5, 16], [5, 18], [5, 19], [6, 7], [6, 11], [6, 13], [7, 4], [7, 6], [7, 9], [7, 11], [7, 13], [8, 2], [8, 16], [9, 1], [9, 4], [9, 7], [9, 13], [9, 14], [9, 15], [9, 17], [10, 3], [10, 12], [10, 18], [10, 19], [11, 1], [11, 4], [11, 5], [11, 6], [11, 7], [12, 3], [12, 10], [12, 14], [12, 18], [13, 6], [13, 7], [13, 9], [13, 15], [14, 1], [14, 3], [14, 9], [14, 12], [14, 17], [14, 18], [15, 9], [15, 13], [15, 17], [16, 2], [16, 5], [16, 8], [16, 19], [17, 3], [17, 9], [17, 14], [17, 15], [18, 1], [18, 5], [18, 10], [18, 12], [18, 14], [18, 19], [19, 2], [19, 5], [19, 10], [19, 16], [19, 18]], 'known_colours': {'1': 'Red', '2': 'Green', '3': 'Blue', '4': 'Yellow', '5': 'Yellow', '6': 'Yellow', '7': 'Blue', '8': 'Red', '9': 'Green', '10': 'Yellow', '11': 'Green', '12': 'Red', '13': 'Red', '14': 'Yellow'}, 'possible_colours_of_unknown': [{'15': 'Blue', '16': 'Blue', '17': 'Red', '18': 'Green', '19': 'Red'}, {'15': 'Yellow', '16': 'Blue', '17': 'Red', '18': 'Green', '19': 'Red'}, {'15': 'Blue', '16': 'Blue', '17': 'Red', '18': 'Blue', '19': 'Red'}, {'15': 'Yellow', '16': 'Blue', '17': 'Red', '18': 'Blue', '19': 'Red'}], 'unique_maps': 4, 'total_regions': 19, 'known_regions': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], 'unknown_regions': [15, 16, 17, 18, 19]} |
|
You are playing a Tower of Hanoi game with 3 rods and 6 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"6",
"3",
"1",
"4"
] | 6 | {'start_position': [[], [3, 2], [6, 5, 4, 1]], 'end_position': [[4, 3], [], [6, 5, 2, 1]], 'moves': [{'position': [[], [3, 2], [6, 5, 4, 1]], 'num_moves': 0}, {'position': [[], [3, 2, 1], [6, 5, 4]], 'num_moves': 1}, {'position': [[4], [3, 2, 1], [6, 5]], 'num_moves': 2}, {'position': [[4, 1], [3, 2], [6, 5]], 'num_moves': 3}, {'position': [[4, 1], [3], [6, 5, 2]], 'num_moves': 4}, {'position': [[4], [3], [6, 5, 2, 1]], 'num_moves': 5}, {'position': [[4, 3], [], [6, 5, 2, 1]], 'num_moves': 6}]} |
|
The board shown in the image is a sliding puzzle of 4 * 4 tile dimensions. It has 15 numbered tiles and one unoccupied (open) position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. All tiles always stay and move inside the red boundary wall, as shown in the image. A move is defined as moving the open position by one tile unit in any available direction. You start from the board position shown in the image and perform exactly 2 moves such that the open position is seen moving in the following sequence: up, down. What is the sum of numbers of the row which now has the open position? | [
"14",
"44",
"23",
"1"
] | 23 | {'starting_grid': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 10, 6, 0]], 'total_moves': 2, 'path_track': {'left, left': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 0, 10, 6]], 'left, right': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 10, 6, 0]], 'left, up': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 0, 14], [7, 10, 3, 6]], 'up, left': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 0, 3], [7, 10, 6, 14]], 'up, up': [[4, 12, 11, 9], [13, 8, 1, 0], [2, 15, 3, 5], [7, 10, 6, 14]], 'up, down': [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 10, 6, 0]]}, 'possible_states': [[[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 0, 10, 6]], [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 10, 6, 0]], [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 0, 14], [7, 10, 3, 6]], [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 0, 3], [7, 10, 6, 14]], [[4, 12, 11, 9], [13, 8, 1, 0], [2, 15, 3, 5], [7, 10, 6, 14]], [[4, 12, 11, 9], [13, 8, 1, 5], [2, 15, 3, 14], [7, 10, 6, 0]]], 'unique_positions': 5} |
|
A 3 * 3 Rubik's Cube has six different coloured panels: red, green, blue, yellow, orange, and grey. The initial state of the cube in terms of the different colour positions in its six faces is shown in the image. To represent the movements of the cube we use six letters: U for Up, D for Down, L for Left, R for Right, F for Front, B for Back. These letters are used in sequence where you need to perform each letter in the sequence from left to right. Each letter tells you to move that face clockwise by 90 degrees. A number 'n' immediately after a letter denotes that you need to move that face clockwise by 90 * n degrees. For example, 'U R3' would mean rotating the up face 90 degrees clockwise and then rotating the right face 270 degrees clockwise. You perform the move sequence 'D B2 D3' starting from the state shown in the image. What would be the number of small 1 * 1 green squares in the back face after completing the move sequence? | [
"2",
"5",
"8",
"3"
] | 5 | {'moves': 'D B2 D3', 'query_face': 'back', 'query_colour': 'green', 'start_position': {'left': [['yellow', 'yellow', 'yellow'], ['yellow', 'yellow', 'yellow'], ['yellow', 'yellow', 'yellow']], 'right': [['orange', 'orange', 'orange'], ['orange', 'orange', 'orange'], ['orange', 'orange', 'orange']], 'down': [['blue', 'blue', 'blue'], ['blue', 'blue', 'blue'], ['blue', 'blue', 'blue']], 'up': [['red', 'red', 'red'], ['red', 'red', 'red'], ['red', 'red', 'red']], 'back': [['green', 'green', 'green'], ['green', 'green', 'green'], ['green', 'green', 'green']], 'front': [['grey', 'grey', 'grey'], ['grey', 'grey', 'grey'], ['grey', 'grey', 'grey']]}, 'end_position': {'left': [['grey', 'yellow', 'yellow'], ['orange', 'yellow', 'yellow'], ['yellow', 'yellow', 'yellow']], 'right': [['orange', 'orange', 'green'], ['orange', 'orange', 'yellow'], ['green', 'green', 'green']], 'down': [['blue', 'blue', 'red'], ['blue', 'blue', 'red'], ['blue', 'blue', 'red']], 'up': [['blue', 'blue', 'blue'], ['red', 'red', 'red'], ['red', 'red', 'red']], 'back': [['orange', 'orange', 'orange'], ['green', 'green', 'green'], ['orange', 'green', 'green']], 'front': [['grey', 'grey', 'grey'], ['grey', 'grey', 'grey'], ['grey', 'grey', 'yellow']]}} |
|
You are given an incomplete map of a country having 15 different regions. The objective is to colour the regions of the map using only the four available colours: red, green, blue and yellow, such that no two adjacent regions have the same colour. Adjacent regions are defined as two regions that share a common boundary of non-zero length. The regions indicated by numbers 1 to 10 have already been coloured, as shown in the image. The regions indicated by numbers 11 to 15 are shown in white as they are yet to be coloured. You need to assign colours to these regions in a way such that it doesn't violate the objective. Each unique colour combination of the regions would result in a unique complete map. How many unique complete maps can be created by colouring all the white regions starting from the given incomplete map? | [
"2",
"7",
"3",
"8"
] | 2 | {'polygon_vertices': {'1': [[0.53251, 0.09773], [0.45099, 0.3454], [0.51158, 0.35578], [0.62593, 0.27381], [0.59701, 0.05676]], '2': [[0.85844, 0.19219], [0.86972, 0.44671], [0.69837, 0.59519], [0.51158, 0.35578], [0.62593, 0.27381]], '3': [[0.59701, 0.05676], [0.62593, 0.27381], [0.85844, 0.19219], [1.0, 0.00663], [1.0, 0.0], [0.6203, 0.0]], '4': [[0.0, 0.09239], [0.30744, 0.24489], [0.46675, 0.05916], [0.47868, 0.0], [0.0, 0.0]], '5': [[0.64613, 0.79694], [1.0, 0.88029], [1.0, 0.93469], [0.57659, 0.88868]], '6': [[0.46675, 0.05916], [0.53251, 0.09773], [0.59701, 0.05676], [0.6203, 0.0], [0.47868, 0.0]], '7': [[0.69837, 0.59519], [0.86972, 0.44671], [1.0, 0.49305], [1.0, 0.6985], [0.70043, 0.69375]], '8': [[0.64613, 0.79694], [0.70043, 0.69375], [1.0, 0.6985], [1.0, 0.88029]], '9': [[0.43303, 0.34497], [0.30744, 0.24489], [0.46675, 0.05916], [0.53251, 0.09773], [0.45099, 0.3454]], '10': [[0.1967, 0.70455], [0.26154, 0.69738], [0.57601, 0.88933], [0.57543, 1.0], [0.0, 1.0], [0.0, 0.82815]], '11': [[1.0, 1.0], [1.0, 0.93469], [0.57659, 0.88868], [0.57601, 0.88933], [0.57543, 1.0]], '12': [[0.70043, 0.69375], [0.69837, 0.59519], [0.51158, 0.35578], [0.45099, 0.3454], [0.43303, 0.34497], [0.26154, 0.69738], [0.57601, 0.88933], [0.57659, 0.88868], [0.64613, 0.79694]], '13': [[0.0, 0.22729], [0.0, 0.09239], [0.30744, 0.24489], [0.43303, 0.34497], [0.26154, 0.69738], [0.1967, 0.70455]], '14': [[0.0, 0.82815], [0.1967, 0.70455], [0.0, 0.22729]], '15': [[0.86972, 0.44671], [1.0, 0.49305], [1.0, 0.00663], [0.85844, 0.19219]]}, 'polygon_adjacency_list': [[1, 2], [1, 3], [1, 6], [1, 9], [1, 12], [2, 1], [2, 3], [2, 7], [2, 12], [2, 15], [3, 1], [3, 2], [3, 6], [3, 15], [4, 6], [4, 9], [4, 13], [5, 8], [5, 11], [5, 12], [6, 1], [6, 3], [6, 4], [6, 9], [7, 2], [7, 8], [7, 12], [7, 15], [8, 5], [8, 7], [8, 12], [9, 1], [9, 4], [9, 6], [9, 12], [9, 13], [10, 11], [10, 12], [10, 13], [10, 14], [11, 5], [11, 10], [11, 12], [12, 1], [12, 2], [12, 5], [12, 7], [12, 8], [12, 9], [12, 10], [12, 11], [12, 13], [13, 4], [13, 9], [13, 10], [13, 12], [13, 14], [14, 10], [14, 13], [15, 2], [15, 3], [15, 7]], 'known_colours': {'1': 'Red', '2': 'Green', '3': 'Blue', '4': 'Blue', '5': 'Green', '6': 'Yellow', '7': 'Red', '8': 'Blue', '9': 'Green', '10': 'Blue'}, 'possible_colours_of_unknown': [{'11': 'Red', '12': 'Yellow', '13': 'Red', '14': 'Yellow', '15': 'Yellow'}, {'11': 'Red', '12': 'Yellow', '13': 'Red', '14': 'Green', '15': 'Yellow'}], 'unique_maps': 2, 'total_regions': 15, 'known_regions': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'unknown_regions': [11, 12, 13, 14, 15]} |
|
A storekeeper is a puzzle in which the player pushes boxes around in a warehouse trying to get them to target locations. The game is represented by an 6 x 6 grid of characters grid where each element is a wall, floor, or box. Your task is to move the box to the end flag under the following rules:
1. The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box by 1 grid. This is a push.
2. The player cannot walk through the box.
What is the minimum number of pushes to move the box to the end flag. | [
"4",
"2",
"3",
"1"
] | 3 | {'ids': {'empty': '.', 'brick': '#', 'box': 'B', 'person': 'S', 'target': 'T'}, 'timestep': {'grid_0': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '#', 'T', '#'], ['#', '.', 'B', '.', '.', '#'], ['#', '.', '.', 'S', '.', '#'], ['#', '.', '.', '.', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_1': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '#', 'T', '#'], ['#', '.', 'S', 'B', '.', '#'], ['#', '.', '.', '', '.', '#'], ['#', '.', '.', '.', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_2': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '#', 'T', '#'], ['#', '.', '', 'S', 'B', '#'], ['#', '.', '.', '', '.', '#'], ['#', '.', '.', '.', '.', '#'], ['#', '#', '#', '#', '#', '#']], 'grid_3': [['#', '#', '#', '#', '#', '#'], ['#', '#', '.', '#', 'B', '#'], ['#', '.', '', '.', 'S', '#'], ['#', '.', '.', '', '.', '#'], ['#', '.', '.', '.', '.', '#'], ['#', '#', '#', '#', '#', '#']]}, 'target': [1, 4], 'box_location': [[2, 2], [2, 3], [2, 4], [1, 4]]} |
|
You are given an 8 * 8 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 8 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 6 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"8",
"7",
"5",
"3"
] | 3 | {'rows': 8, 'columns': 8, 'given_queen_positions': [[0, 0], [1, 6], [2, 4], [3, 7], [4, 1], [7, 2]], 'missing_queen_positions': [[5, 3], [6, 5]]} |
|
You are given an 8 * 8 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 8 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 6 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"7",
"9",
"6",
"8"
] | 7 | {'rows': 8, 'columns': 8, 'given_queen_positions': [[1, 2], [2, 7], [3, 1], [4, 4], [5, 0], [7, 3]], 'missing_queen_positions': [[0, 6], [6, 5]]} |
|
A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1635 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize? | [
"Laptop",
"Chocolate",
"Ice Cream",
"Watch"
] | Watch | {'angles': [30, 30, 30, 45, 75, 90, 30, 30], 'arrow_at': 135, 'effective_rotation': 195, 'direction': 'counterclockwise', 'original_colors': ['magenta', 'forestgreen', 'darkorange', 'cyan', 'blanchedalmond', 'silver', 'yellow', 'royalblue'], 'original_boundaries': [45.0, 75.0, 105.0, 135.0, 180.0, 255.0, 345.0, 375.0], 'original_prizes': ['Camera', 'Yacht', 'Jewelry', 'Laptop', 'Vacation', 'Watch', 'Chocolate', 'Ice Cream'], 'rotated_colors': ['blanchedalmond', 'silver', 'yellow', 'royalblue', 'magenta', 'forestgreen', 'darkorange', 'cyan'], 'rotated_boundaries': [15.0, 90.0, 180.0, 210.0, 240.0, 270.0, 300.0, 330.0], 'rotated_prizes': ['Vacation', 'Watch', 'Chocolate', 'Ice Cream', 'Camera', 'Yacht', 'Jewelry', 'Laptop']} |
|
A 4 * 5 board consists of 20 different coloured tiles. A random state of the board is shown in (A). The ideal state of the board is shown in (B). A swap consists of selecting any two tiles on the board and switching their positions. What is the minimum number of swaps required to restore the ideal state of the board from (A)? | [
"3",
"4",
"5",
"1"
] | 4 | {'ideal_grid': [[[255, 105, 180], [255, 134, 181], [255, 163, 182], [255, 192, 183], [255, 221, 186]], [[206, 93, 152], [214, 116, 152], [222, 139, 152], [229, 163, 153], [238, 186, 154]], [[157, 81, 124], [173, 98, 123], [189, 115, 122], [203, 134, 123], [221, 151, 122]], [[108, 67, 94], [131, 79, 93], [154, 91, 92], [177, 103, 91], [203, 115, 88]]], 'shuffled_grid': [[[255, 105, 180], [173, 98, 123], [255, 163, 182], [255, 192, 183], [255, 221, 186]], [[206, 93, 152], [214, 116, 152], [222, 139, 152], [229, 163, 153], [238, 186, 154]], [[157, 81, 124], [154, 91, 92], [189, 115, 122], [255, 134, 181], [131, 79, 93]], [[108, 67, 94], [221, 151, 122], [203, 134, 123], [177, 103, 91], [203, 115, 88]]], 'shuffled_order': [0, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 12, 1, 16, 15, 14, 13, 18, 19], 'swaps': 4, 'in_position': 14, 'out_of_position': 6} |
|
You are playing a Tower of Hanoi game with 3 rods and 4 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"5",
"4",
"2",
"6"
] | 2 | {'start_position': [[], [3, 2], [4, 1]], 'end_position': [[2, 1], [3], [4]], 'moves': [{'position': [[], [3, 2], [4, 1]], 'num_moves': 0}, {'position': [[2], [3], [4, 1]], 'num_moves': 1}, {'position': [[2, 1], [3], [4]], 'num_moves': 2}]} |
|
Consider a sliding block puzzle of grid size 5 * 4 units. It has 9 wooden blocks of varying sizes: one 2 * 2, four 1 * 2, two 2 * 1, and two 1 * 1. The gird also has two empty 1 * 1 spaces. The blocks cannot be removed from the grid, and may only be slid horizontally and vertically within its boundary. A move is defined as selecting a block that is slideable, and moving it by 1 unit either horizontally or vertically, whichever is possible. The image shows the starting and ending configurations of the puzzle grid. The wooden blocks are shown in various shades of brown and the empty spaces are shown in white. What is the minimum number of moves required to reach the ending configuration from the starting configuration? | [
"2",
"1",
"5",
"4"
] | 5 | {'start_position': '2233\n6114\n6115\n0788\n0799', 'end_position': '2233\n6110\n6114\n7885\n7990', 'moves': ['2233\n6114\n6115\n0788\n0799', '2233\n6114\n6115\n7088\n7099', '2233\n6114\n6115\n7880\n7099', '2233\n6114\n6110\n7885\n7099', '2233\n6110\n6114\n7885\n7099', '2233\n6110\n6114\n7885\n7990']} |
|
You are given an 8 * 8 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 8 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 6 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"12",
"10",
"7",
"3"
] | 10 | {'rows': 8, 'columns': 8, 'given_queen_positions': [[0, 5], [1, 2], [3, 1], [4, 3], [5, 7], [7, 4]], 'missing_queen_positions': [[2, 6], [6, 0]]} |
|
You are given an 8 * 8 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 8 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 6 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"13",
"8",
"5",
"4"
] | 8 | {'rows': 8, 'columns': 8, 'given_queen_positions': [[0, 1], [2, 7], [3, 2], [5, 3], [6, 6], [7, 4]], 'missing_queen_positions': [[1, 5], [4, 0]]} |
|
You are given a 9 * 9 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 9 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 7 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"9",
"10",
"3",
"12"
] | 3 | {'rows': 9, 'columns': 9, 'given_queen_positions': [[0, 2], [1, 0], [3, 7], [5, 1], [6, 3], [7, 8], [8, 6]], 'missing_queen_positions': [[2, 5], [4, 4]]} |
|
Consider a sliding block puzzle of grid size 5 * 4 units. It has 9 wooden blocks of varying sizes: one 2 * 2, four 1 * 2, two 2 * 1, and two 1 * 1. The gird also has two empty 1 * 1 spaces. The blocks cannot be removed from the grid, and may only be slid horizontally and vertically within its boundary. A move is defined as selecting a block that is slideable, and moving it by 1 unit either horizontally or vertically, whichever is possible. The image shows the starting and ending configurations of the puzzle grid. The wooden blocks are shown in various shades of brown and the empty spaces are shown in white. What is the minimum number of moves required to reach the ending configuration from the starting configuration? | [
"2",
"1",
"5",
"4"
] | 4 | {'start_position': '0633\n0622\n7115\n7114\n8899', 'end_position': '6033\n6225\n7114\n7110\n8899', 'moves': ['0633\n0622\n7115\n7114\n8899', '6033\n6022\n7115\n7114\n8899', '6033\n6220\n7115\n7114\n8899', '6033\n6225\n7110\n7114\n8899', '6033\n6225\n7114\n7110\n8899']} |
|
The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No. | [
"Yes",
"No"
] | No | {'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[4, 4], [5, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"6",
"5",
"3",
"1"
] | 3 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 1, 1], [0, 1, 1], [1, 1, 2]], 'minute_1': [[0, 1, 1], [0, 1, 2], [1, 2, 2]], 'minute_2': [[0, 1, 2], [0, 2, 2], [2, 2, 2]], 'minute_3': [[0, 2, 2], [0, 2, 2], [2, 2, 2]]}} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"2",
"6",
"5",
"1"
] | 2 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 1, 1], [1, 2, 1], [1, 1, 0]], 'minute_1': [[0, 2, 1], [2, 2, 2], [1, 2, 0]], 'minute_2': [[0, 2, 2], [2, 2, 2], [2, 2, 0]]}} |
|
The board shown in the image is a sliding puzzle of 3 * 3 tile dimensions. It has 8 numbered tiles and one unoccupied (open) position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. All tiles always stay and move inside the red boundary wall, as shown in the image. A move is defined as moving the open position by one tile unit in any available direction. You start from the board position shown in the image and perform exactly 4 moves. What is the maximum sum that you can achieve across the bottom most row in the final board position? | [
"17",
"6",
"30",
"40"
] | 17 | {'starting_grid': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'total_moves': 4, 'path_track': {'left, left, right, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, left, right, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, left, right, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, left, right, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'left, left, up, right': [[8, 0, 1], [3, 2, 6], [4, 5, 7]], 'left, left, up, down': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, left, down, right': [[3, 8, 1], [4, 2, 6], [5, 0, 7]], 'left, left, down, up': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, right, left, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, right, left, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, right, left, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, right, left, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'left, right, up, left': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'left, right, up, down': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, right, down, left': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'left, right, down, up': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, up, left, right': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, up, left, down': [[2, 3, 1], [0, 8, 6], [4, 5, 7]], 'left, up, right, left': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, up, right, down': [[3, 1, 6], [2, 8, 0], [4, 5, 7]], 'left, up, down, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, up, down, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, up, down, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, up, down, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'left, down, left, right': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'left, down, left, up': [[3, 8, 1], [0, 5, 6], [2, 4, 7]], 'left, down, right, left': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'left, down, right, up': [[3, 8, 1], [2, 5, 0], [4, 7, 6]], 'left, down, up, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'left, down, up, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'left, down, up, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'left, down, up, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'up, left, left, right': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'up, left, left, down': [[2, 3, 8], [0, 6, 1], [4, 5, 7]], 'up, left, right, left': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'up, left, right, down': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'up, left, down, left': [[3, 6, 8], [0, 2, 1], [4, 5, 7]], 'up, left, down, right': [[3, 6, 8], [2, 1, 0], [4, 5, 7]], 'up, left, down, up': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'up, left, down, down': [[3, 6, 8], [2, 5, 1], [4, 0, 7]], 'up, down, left, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'up, down, left, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'up, down, left, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'up, down, left, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'up, down, up, left': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'up, down, up, down': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'up, down, down, left': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'up, down, down, up': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'down, left, left, right': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'down, left, left, up': [[3, 8, 1], [0, 6, 7], [2, 4, 5]], 'down, left, right, left': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'down, left, right, up': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'down, left, up, left': [[3, 8, 1], [0, 2, 7], [4, 6, 5]], 'down, left, up, right': [[3, 8, 1], [2, 7, 0], [4, 6, 5]], 'down, left, up, up': [[3, 0, 1], [2, 8, 7], [4, 6, 5]], 'down, left, up, down': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'down, up, left, left': [[3, 8, 1], [0, 2, 6], [4, 5, 7]], 'down, up, left, right': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'down, up, left, up': [[3, 0, 1], [2, 8, 6], [4, 5, 7]], 'down, up, left, down': [[3, 8, 1], [2, 5, 6], [4, 0, 7]], 'down, up, up, left': [[3, 0, 8], [2, 6, 1], [4, 5, 7]], 'down, up, up, down': [[3, 8, 1], [2, 6, 0], [4, 5, 7]], 'down, up, down, left': [[3, 8, 1], [2, 6, 7], [4, 0, 5]], 'down, up, down, up': [[3, 8, 1], [2, 6, 0], [4, 5, 7]]}, 'possible_states': [[[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[8, 0, 1], [3, 2, 6], [4, 5, 7]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [4, 2, 6], [5, 0, 7]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[2, 3, 1], [0, 8, 6], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 1, 6], [2, 8, 0], [4, 5, 7]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 8, 1], [0, 5, 6], [2, 4, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 8, 1], [2, 5, 0], [4, 7, 6]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[2, 3, 8], [0, 6, 1], [4, 5, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 6, 8], [0, 2, 1], [4, 5, 7]], [[3, 6, 8], [2, 1, 0], [4, 5, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[3, 6, 8], [2, 5, 1], [4, 0, 7]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [0, 6, 7], [2, 4, 5]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 8, 1], [0, 2, 7], [4, 6, 5]], [[3, 8, 1], [2, 7, 0], [4, 6, 5]], [[3, 0, 1], [2, 8, 7], [4, 6, 5]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [0, 2, 6], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 0, 1], [2, 8, 6], [4, 5, 7]], [[3, 8, 1], [2, 5, 6], [4, 0, 7]], [[3, 0, 8], [2, 6, 1], [4, 5, 7]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]], [[3, 8, 1], [2, 6, 7], [4, 0, 5]], [[3, 8, 1], [2, 6, 0], [4, 5, 7]]], 'unique_positions': 20} |
|
This is maze having 11 * 9 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. How many cells do you need to visit in this optimal path including the entrance and exit cells? | [
"45",
"22",
"31",
"37"
] | 37 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [2, 5], [1, 5], [1, 6], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [5, 6], [5, 5], [6, 5], [7, 5], [7, 4], [7, 3], [6, 3], [5, 3], [5, 2], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [9, 2], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7], [9, 8]], 'optimal_path_length': 37, 'left_turns': 6, 'right_turns': 6, 'total_turns': 12} |
|
A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.35 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize? | [
"Jewelry",
"Chocolate",
"Yacht",
"Pizza"
] | Jewelry | {'angles': [30, 30, 75, 60, 30, 60, 30, 45], 'arrow_at': 0, 'effective_rotation': -234, 'direction': 'clockwise', 'original_colors': ['cyan', 'silver', 'blanchedalmond', 'darkorange', 'lime', 'yellow', 'forestgreen', 'magenta'], 'original_boundaries': [45.0, 75.0, 105.0, 180.0, 240.0, 270.0, 330.0, 360.0], 'original_prizes': ['Money', 'Chocolate', 'Jewelry', 'Car', 'Pizza', 'Yacht', 'Laptop', 'Vacation'], 'rotated_colors': ['darkorange', 'lime', 'yellow', 'forestgreen', 'magenta', 'cyan', 'silver', 'blanchedalmond'], 'rotated_boundaries': [54.0, 114.0, 144.0, 204.0, 234.0, 279.0, 309.0, 339.0], 'rotated_prizes': ['Car', 'Pizza', 'Yacht', 'Laptop', 'Vacation', 'Money', 'Chocolate', 'Jewelry']} |
|
This is maze having 7 * 11 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of left turns do you need to make in this optimal path? | [
"4",
"5",
"1",
"3"
] | 3 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [4, 5], [3, 5], [3, 6], [3, 7], [2, 7], [1, 7], [1, 8], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9]], 'optimal_path_length': 23, 'left_turns': 3, 'right_turns': 4, 'total_turns': 7} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"5",
"2",
"4",
"3"
] | 3 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 0, 0], [1, 1, 0], [0, 2, 0]], 'minute_1': [[1, 0, 0], [1, 2, 0], [0, 2, 0]], 'minute_2': [[1, 0, 0], [2, 2, 0], [0, 2, 0]], 'minute_3': [[2, 0, 0], [2, 2, 0], [0, 2, 0]]}} |
|
You are playing a Tower of Hanoi game with 3 rods and 3 disks of various diameters, which can slide onto any rod. You are given the starting and ending configuration of the game as shown in the top and the bottom of the image, respectively. The game has the following rules: i) Only one disk may be moved at a time; ii) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; and iii) No disk can be placed on top of a disk that is smaller than it. What is the minimum number of moves required to go from the starting to the ending configuration? | [
"5",
"1",
"3",
"6"
] | 1 | {'start_position': [[], [], [3, 2, 1]], 'end_position': [[1], [], [3, 2]], 'moves': [{'position': [[], [], [3, 2, 1]], 'num_moves': 0}, {'position': [[1], [], [3, 2]], 'num_moves': 1}]} |
|
You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"3",
"6",
"1",
"4"
] | 3 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[0, 2, 0], [1, 1, 1], [1, 0, 0]], 'minute_1': [[0, 2, 0], [1, 2, 1], [1, 0, 0]], 'minute_2': [[0, 2, 0], [2, 2, 2], [1, 0, 0]], 'minute_3': [[0, 2, 0], [2, 2, 2], [2, 0, 0]]}} |
|
You are given 4 jugs of capacities 12, 7, 4, 2 litres. Initially, the amount of water that is contained in each jar is shown in the image. A single step of water pouring from one jug to another is constrained by the following rules: i) take a non-empty jug and pour water from it to another non-full jug until the first one becomes empty or the second one becomes full; and ii) no water can be split while pouring. The objective is to reach the amounts of 7, 5, 4, 2 litres of water in the jugs from left to right, respectively. What is the minimum number of water pouring steps required to achieve the objective? | [
"2",
"1",
"3",
"6"
] | 1 | {'num_jugs': 4, 'capacities': [12, 7, 4, 2], 'total_water': 18, 'start': [9, 5, 2, 2], 'end': [7, 5, 4, 2], 'steps': [[9, 5, 2, 2], [7, 5, 4, 2]], 'num_steps': 1} |
|
A 1 * 5 board consists of 5 different coloured tiles. A random state of the board is shown in (A). The ideal state of the board is shown in (B). A swap consists of selecting any two tiles on the board and switching their positions. What is the minimum number of swaps required to restore the ideal state of the board from (A)? | [
"1",
"4",
"2",
"5"
] | 2 | {'ideal_grid': [[[255, 111, 60], [255, 133, 60], [255, 155, 60], [255, 177, 60], [255, 201, 60]]], 'shuffled_grid': [[[255, 201, 60], [255, 155, 60], [255, 133, 60], [255, 177, 60], [255, 111, 60]]], 'shuffled_order': [4, 2, 1, 3, 0], 'swaps': 2, 'in_position': 1, 'out_of_position': 4} |
|
Alice has 9 segments of chains of different lengths as shown in the image. The total length of all the segments combined is 22 pieces. She has a saw machine with which a closed piece can be cut opened. She also has a welding machine with which an open piece can be closed. Each cut takes 4 minutes and each welding takes 5 minutes. Initially, she has 4 segments each with 1 open piece as shown in the image. All the other pieces are closed. She now wants to make the longest possible necklace using all the available 22 pieces. Each piece in the necklace would be connected to exactly two other pieces. This would require cutting open some pieces and then joining all the resulting segments together. What is the minimum time in which she can create the necklace? | [
"29",
"27",
"48",
"21"
] | 29 | {'steps': [[4, 0, 1, 2, 0, 2], [5, 1, 0, 2, 0, 2]], 'cuts': 1, 'joins': 5, 'each_cut_time': 4, 'each_join_time': 5, 'total_time': 29} |
|
A 5 * 4 board consists of 20 different coloured tiles. A random state of the board is shown in (A). The ideal state of the board is shown in (B). A swap consists of selecting any two tiles on the board and switching their positions. What is the minimum number of swaps required to restore the ideal state of the board from (A)? | [
"7",
"6",
"9",
"3"
] | 7 | {'ideal_grid': [[[255, 182, 0], [255, 156, 59], [255, 130, 118], [255, 102, 178]], [[242, 166, 22], [235, 142, 66], [227, 119, 112], [219, 94, 157]], [[229, 150, 44], [215, 128, 73], [199, 108, 106], [183, 86, 136]], [[216, 134, 66], [195, 114, 80], [171, 97, 100], [147, 78, 115]], [[203, 115, 88], [172, 99, 90], [141, 83, 92], [108, 67, 94]]], 'shuffled_grid': [[[255, 130, 118], [255, 156, 59], [199, 108, 106], [255, 102, 178]], [[242, 166, 22], [235, 142, 66], [219, 94, 157], [229, 150, 44]], [[108, 67, 94], [215, 128, 73], [216, 134, 66], [183, 86, 136]], [[255, 182, 0], [195, 114, 80], [171, 97, 100], [147, 78, 115]], [[203, 115, 88], [172, 99, 90], [227, 119, 112], [141, 83, 92]]], 'shuffled_order': [2, 1, 10, 3, 4, 5, 7, 8, 19, 9, 12, 11, 0, 13, 14, 15, 16, 17, 6, 18], 'swaps': 7, 'in_position': 11, 'out_of_position': 9} |
|
A checker game is being played on a grid of 10 squares with 4 green and 5 red checkers. Initially, the checkers are arranged as shown in the starting configuration with the 9 checkers occupying 9 squares and one unoccupied square. Green checkers only move rightward and red checkers only move leftward. Every move is either i) a slide to the adjacent empty square, or ii) a jump over one position to an empty square, provided the checker being jumped over is of a different colour. Each square can accommodate a maximum of one checker at any time. How many moves are required to reach the ending configuration from the starting configuration following the specified rules? | [
"2",
"5",
"3",
"0"
] | 3 | {'start_position': 'RRGRG_GRGR', 'end_position': 'RRGRGRGR_G', 'green_checkers': 4, 'red_checkers': 5, 'moves': ['RRGRG_GRGR', 'RRGRGRG_GR', 'RRGRGRGRG_', 'RRGRGRGR_G']} |
|
You are given a 9 * 9 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 9 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 7 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"14",
"5",
"8",
"7"
] | 8 | {'rows': 9, 'columns': 9, 'given_queen_positions': [[0, 2], [1, 8], [2, 3], [4, 4], [6, 5], [7, 0], [8, 6]], 'missing_queen_positions': [[3, 7], [5, 1]]} |
|
A 3 * 3 Rubik's Cube has six different coloured panels: red, green, blue, yellow, orange, and grey. The initial state of the cube in terms of the different colour positions in its six faces is shown in the image. To represent the movements of the cube we use six letters: U for Up, D for Down, L for Left, R for Right, F for Front, B for Back. These letters are used in sequence where you need to perform each letter in the sequence from left to right. Each letter tells you to move that face clockwise by 90 degrees. A number 'n' immediately after a letter denotes that you need to move that face clockwise by 90 * n degrees. For example, 'U R3' would mean rotating the up face 90 degrees clockwise and then rotating the right face 270 degrees clockwise. You perform the move sequence 'F3' starting from the state shown in the image. What would be the number of small 1 * 1 yellow squares in the down face after completing the move sequence? | [
"4",
"0",
"7",
"2"
] | 2 | {'moves': 'F3', 'query_face': 'down', 'query_colour': 'yellow', 'start_position': {'left': [['grey', 'green', 'yellow'], ['blue', 'blue', 'red'], ['orange', 'green', 'red']], 'right': [['red', 'green', 'red'], ['blue', 'green', 'green'], ['yellow', 'yellow', 'orange']], 'down': [['orange', 'orange', 'grey'], ['red', 'orange', 'grey'], ['grey', 'yellow', 'red']], 'up': [['blue', 'orange', 'green'], ['yellow', 'yellow', 'grey'], ['green', 'orange', 'blue']], 'back': [['yellow', 'red', 'orange'], ['orange', 'red', 'yellow'], ['green', 'red', 'green']], 'front': [['grey', 'grey', 'yellow'], ['blue', 'grey', 'grey'], ['blue', 'blue', 'blue']]}, 'end_position': {'left': [['grey', 'green', 'blue'], ['blue', 'blue', 'orange'], ['orange', 'green', 'green']], 'right': [['grey', 'green', 'red'], ['orange', 'green', 'green'], ['orange', 'yellow', 'orange']], 'down': [['yellow', 'red', 'red'], ['red', 'orange', 'grey'], ['grey', 'yellow', 'red']], 'up': [['blue', 'orange', 'green'], ['yellow', 'yellow', 'grey'], ['red', 'blue', 'yellow']], 'back': [['yellow', 'red', 'orange'], ['orange', 'red', 'yellow'], ['green', 'red', 'green']], 'front': [['yellow', 'grey', 'blue'], ['grey', 'grey', 'blue'], ['grey', 'blue', 'blue']]}} |
|
Jessica came to an event 32 minutes ago. The current time is shown on the clock. The clock is a standard analog clock without the seconds hand. What was the time when Jessica came to the event? | [
"8:20",
"10:31",
"2:30",
"2:02"
] | 2:02 | {'current_hour': 2, 'current_minute': 34, 'subtract_hour': 0, 'subtract_minute': 32} |
|
This is maze having 11 * 9 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. How many cells do you need to visit in this optimal path including the entrance and exit cells? | [
"5",
"21",
"35",
"6"
] | 21 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [9, 2], [9, 3], [8, 3], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], [8, 7], [9, 7], [9, 8]], 'optimal_path_length': 21, 'left_turns': 3, 'right_turns': 3, 'total_turns': 6} |
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You are given a 3 x 3 grid in which each cell can contain either no kiwi, one fresh kiwi, or one rotten kiwi. Every minute, any fresh kiwi that is 4-directionally adjacent to a rotten kiwi also becomes rotten. What is the minimum number of minutes that must elapse until no cell has a fresh kiwi? | [
"2",
"6",
"4",
"5"
] | 4 | {'ids': {'empty': 0, 'fresh': 1, 'rotten': 2}, 'timestep': {'minute_0': [[1, 0, 2], [1, 1, 1], [1, 0, 1]], 'minute_1': [[1, 0, 2], [1, 1, 2], [1, 0, 1]], 'minute_2': [[1, 0, 2], [1, 2, 2], [1, 0, 2]], 'minute_3': [[1, 0, 2], [2, 2, 2], [1, 0, 2]], 'minute_4': [[2, 0, 2], [2, 2, 2], [2, 0, 2]]}} |
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A 3 * 3 Rubik's Cube has six different coloured panels: red, green, blue, yellow, orange, and grey. The initial state of the cube in terms of the different colour positions in its six faces is shown in the image. To represent the movements of the cube we use six letters: U for Up, D for Down, L for Left, R for Right, F for Front, B for Back. These letters are used in sequence where you need to perform each letter in the sequence from left to right. Each letter tells you to move that face clockwise by 90 degrees. A number 'n' immediately after a letter denotes that you need to move that face clockwise by 90 * n degrees. For example, 'U R3' would mean rotating the up face 90 degrees clockwise and then rotating the right face 270 degrees clockwise. You perform the move sequence 'D L3 F3' starting from the state shown in the image. What would be the number of small 1 * 1 grey squares in the right face after completing the move sequence? | [
"9",
"7",
"5",
"3"
] | 5 | {'moves': 'D L3 F3', 'query_face': 'right', 'query_colour': 'grey', 'start_position': {'left': [['red', 'red', 'red'], ['red', 'red', 'red'], ['red', 'red', 'red']], 'right': [['grey', 'grey', 'grey'], ['grey', 'grey', 'grey'], ['grey', 'grey', 'grey']], 'down': [['orange', 'orange', 'orange'], ['orange', 'orange', 'orange'], ['orange', 'orange', 'orange']], 'up': [['green', 'green', 'green'], ['green', 'green', 'green'], ['green', 'green', 'green']], 'back': [['yellow', 'yellow', 'yellow'], ['yellow', 'yellow', 'yellow'], ['yellow', 'yellow', 'yellow']], 'front': [['blue', 'blue', 'blue'], ['blue', 'blue', 'blue'], ['blue', 'blue', 'blue']]}, 'end_position': {'left': [['red', 'red', 'green'], ['red', 'red', 'green'], ['red', 'red', 'red']], 'right': [['orange', 'grey', 'grey'], ['orange', 'grey', 'grey'], ['grey', 'blue', 'blue']], 'down': [['yellow', 'yellow', 'yellow'], ['yellow', 'orange', 'orange'], ['yellow', 'orange', 'orange']], 'up': [['blue', 'green', 'green'], ['blue', 'green', 'green'], ['grey', 'grey', 'blue']], 'back': [['yellow', 'yellow', 'green'], ['yellow', 'yellow', 'green'], ['grey', 'grey', 'green']], 'front': [['blue', 'blue', 'red'], ['blue', 'blue', 'red'], ['orange', 'orange', 'orange']]}} |
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A 6 * 4 board consists of 24 different coloured tiles. A random state of the board is shown in (A). The ideal state of the board is shown in (B). A swap consists of selecting any two tiles on the board and switching their positions. What is the minimum number of swaps required to restore the ideal state of the board from (A)? | [
"1",
"2",
"5",
"3"
] | 3 | {'ideal_grid': [[[163, 173, 142], [193, 181, 142], [223, 189, 142], [255, 198, 142]], [[132, 161, 154], [156, 170, 149], [180, 179, 145], [205, 188, 140]], [[101, 149, 166], [119, 159, 156], [137, 169, 148], [155, 178, 138]], [[70, 137, 178], [82, 148, 163], [94, 159, 151], [105, 168, 136]], [[39, 125, 190], [45, 137, 170], [51, 149, 154], [55, 158, 134]], [[4, 113, 205], [4, 124, 181], [4, 135, 157], [3, 146, 132]]], 'shuffled_grid': [[[163, 173, 142], [193, 181, 142], [223, 189, 142], [94, 159, 151]], [[132, 161, 154], [156, 170, 149], [255, 198, 142], [205, 188, 140]], [[101, 149, 166], [119, 159, 156], [137, 169, 148], [155, 178, 138]], [[70, 137, 178], [82, 148, 163], [180, 179, 145], [105, 168, 136]], [[39, 125, 190], [45, 137, 170], [51, 149, 154], [55, 158, 134]], [[4, 113, 205], [4, 135, 157], [4, 124, 181], [3, 146, 132]]], 'shuffled_order': [0, 1, 2, 14, 4, 5, 3, 7, 8, 9, 10, 11, 12, 13, 6, 15, 16, 17, 18, 19, 20, 22, 21, 23], 'swaps': 3, 'in_position': 19, 'out_of_position': 5} |
|
This is maze having 9 * 7 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of left turns do you need to make in this optimal path? | [
"2",
"1",
"4",
"5"
] | 2 | {'maze': [[1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 1], [1, 1, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [5, 3], [6, 3], [7, 3], [7, 4], [7, 5], [7, 6]], 'optimal_path_length': 13, 'left_turns': 2, 'right_turns': 2, 'total_turns': 4} |
|
This is maze having 7 * 13 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of left turns do you need to make in this optimal path? | [
"5",
"1",
"4",
"3"
] | 4 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [2, 1], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [2, 5], [1, 5], [1, 6], [1, 7], [2, 7], [3, 7], [3, 8], [3, 9], [4, 9], [5, 9], [5, 10], [5, 11], [6, 11]], 'optimal_path_length': 21, 'left_turns': 4, 'right_turns': 5, 'total_turns': 9} |
|
A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.2 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize? | [
"Pizza",
"Ice Cream",
"Jewelry",
"Camera"
] | Camera | {'angles': [20, 20, 30, 45, 30, 30, 20, 60, 45, 60], 'arrow_at': 45, 'effective_rotation': -288, 'direction': 'clockwise', 'original_colors': ['darkorange', 'blanchedalmond', 'cyan', 'orangered', 'royalblue', 'silver', 'lime', 'magenta', 'yellow', 'forestgreen'], 'original_boundaries': [45.0, 65.0, 85.0, 115.0, 160.0, 190.0, 220.0, 240.0, 300.0, 345.0], 'original_prizes': ['Pizza', 'Vacation', 'Yacht', 'Camera', 'Chocolate', 'Jewelry', 'Ice Cream', 'Car', 'Money', 'Watch'], 'rotated_colors': ['cyan', 'orangered', 'royalblue', 'silver', 'lime', 'magenta', 'yellow', 'forestgreen', 'darkorange', 'blanchedalmond'], 'rotated_boundaries': [13.0, 43.0, 88.0, 118.0, 148.0, 168.0, 228.0, 273.0, 333.0, 353.0], 'rotated_prizes': ['Yacht', 'Camera', 'Chocolate', 'Jewelry', 'Ice Cream', 'Car', 'Money', 'Watch', 'Pizza', 'Vacation']} |
|
You are given a 10 * 10 chessboard. The Manhattan distance between two squares in a chessboard is equal to the minimal number of orthogonal King moves between these squares on the otherwise empty board. The objective is to place 10 chess queens on this board so that no two queens threaten each other; i.e. no two queens share the same row, column, or diagonal. 8 queens have already been placed in some of the squares of the board, as shown in the image. Suppose you pick two squares to place the two remaining queen pieces in a way that fulfills the objective. What is the Manhattan distance between these two squares? | [
"11",
"9",
"3",
"13"
] | 9 | {'rows': 10, 'columns': 10, 'given_queen_positions': [[1, 4], [2, 6], [3, 0], [4, 9], [6, 8], [7, 2], [8, 7], [9, 3]], 'missing_queen_positions': [[0, 1], [5, 5]]} |
|
This is maze having 7 * 9 cells. The empty cells are coloured white and the obstacle cells are coloured black. From an empty cell, you can only move up, down, left, or right to another adjacent empty cell. You cannot move diagonally between two empty cells and cannot step into a cell with an obstacle. The entry cell of the maze is shown with the green arrow. The exit cell of the maze is shown with the blue arrow. Suppose you have found the most optimal path in the maze between the entrance and exit, where you need to go through the least number of empty cells and you need to make the least number of left and right turns. What is the total number of right turns do you need to make in this optimal path? | [
"1",
"5",
"4",
"3"
] | 3 | {'maze': [[1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1]], 'optimal_path': [[1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 7], [3, 7], [3, 6], [3, 5], [4, 5], [5, 5], [5, 6], [5, 7], [6, 7]], 'optimal_path_length': 17, 'left_turns': 2, 'right_turns': 3, 'total_turns': 5} |
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