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Browse High School Puzzles
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to frequently posed puzzles:
    1000 lockers.
    Letter+number puzzles.
    Getting across the river.
    How many handshakes?
    Last one at the table.
    Monkeys dividing coconuts.
    Remainder/divisibility puzzles.
    Squares in a checkerboard.
    Weighing a counterfeit coin.
    What color is my hat?


Passing Ships [05/12/1999]

Perilous Ping-Pong [11/14/1997]
Weigh the balls to find the one that's different...

The Pharaoh's Will [05/16/2000]

Placing Coins That Touch [8/7/1996]

Planting Trees [08/13/2002]

Pool Table Algebra [10/21/1998]
The y-axis, x-axis, x = 6, and y = 12 determine the sides of a pool table. Follow the path of a ball starting at the point (3,8).

Positive Unit Fractions [10/02/2002]
Find five different positive unit fractions whose sum is 1. (A unit fraction is a fraction whose numerator is 1. All denominators must also be natural numbers.)

Powers of Two [05/29/1997]
Prove that every power of two has a multiple whose decimal expansion has only digits 1 and 2.

Does the orthocenter of a triangle have any practical uses?

The Predetermined Sum Puzzle [02/02/2001]

Preparing for the Putnam Exam [11/04/2004]
I was wondering if you could give me some specific advice on how to study for the Putnam Exam because I will be taking it for my first time.

Prices in Store 88 [07/05/1999]

Prime Factors and Square Products [10/05/2003]
What is the smallest number that you can multiply by 540 to make a square number?

Primes and Number Riddles [4/15/1996]
A prime number riddle.

The Prisoners' Dilemma [12/8/1995]


Puzzle to Find a 10 Digit Number [10/10/2004]
I have to find a 10 digit number which uses each of the digits 0-9 such that the first digit is divisible by 1, the first two digits make a number divisible by 2, the first three digits make a number divisible by 3, and so on up to all ten digits making a number divisible by 10. I figured it out using mostly guess and check, but it took a long time. Is there a quicker way?


Rameses' Pyramid [12/10/1997]
A pyramid-building puzzle.

Rational Number and its Reciprocal [03/14/2002]

Rectangles on a Chessboard [02/09/2002]
How many rectangles are there on a chessboard?

Red Hat, Blue Hat [11/16/2002]

Rubik's Cube [12/03/1998]
Can you explain some of the math behind the Rubik's Cube?

Rubik's Cube [02/18/1999]
Sequences of turns for solving Rubik's cube.

Rubik's Cube Combinations [04/11/2001]

Running Laps [07/03/2002]

Russian Nim [02/15/1999]

Scoring System Problem [10/28/2001]
What is the highest score that is impossible to make?

Sequence Question from IQ Test [06/28/2007]

Set Notation via Broken Typewriter [11/19/2002]
I have a machine that only types out ones (no spaces or tricks involved). What procedure must you do to this machine to get any given finite set? For example [2,85,11,5,60]. For a different set, the number of ones that the machine types out will vary.

Seven Elevators Stop at Six Floors [09/14/2002]
A building has 7 elevators, each stopping on at most 6 floors. If you take the right elevator you can get to any floor from any other floor without changing elevators. What is the greatest number of floors the building can have?

Shuffling Cards [8/26/1996]
How many 'perfect shuffles' does it take to get the cards back in the order you started?

Simultaneous Equations with Integral Solutions [11/29/1996]

Six-Card Trick [10/25/2000]
A Volunteer writes different numbers from 1 to 125 on six cards, and keeps one. The Host arranges the others in some order and gives them to the Partner, who then says the number on the missing card. How?

Snail! [06/20/2002]

Solving a Math Poem [05/24/2000]

Solving Questions [08/28/2002]

I have tried logical reasoning and can't get it.



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