Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

Middle School Archive


This page:
  puzzles checkmark


See also the
Dr. Math FAQ:
  classic problems


About Math

   factoring expressions
   graphing equations

   factoring numbers


     conic sections/
   3D and higher



Number Sense
   factoring numbers
   negative numbers
   prime numbers
   square roots

Word Problems

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

Selected answers to frequently posed puzzles:
    Letter+number puzzles.
    Number sentences.
    Remainder/divisibility puzzles.

    1000 lockers.
    Getting across the river.
    Heads, legs: how many animals?
    A hen and a half...
    How many handshakes?
    Last one at the table.
    Measuring with two containers.
    Monkeys dividing coconuts.
    Squares in a checkerboard.
    Weighing a counterfeit coin.
    What color is my hat?


Product of Numbers 1-100 [02/23/2002]
I was wondering how to find out how many zeros will be at the end of the product of all the numbers from 1 to 100 without multiplying them all out.


Pupil 47 Opposite Pupil 16 in the Circle [09/17/2002]
If, in Mr. Simmons' class, pupil 47 is opposite pupil 16 when the group is seated in a circle, how many students are in the class?

Puzzle with a Difference [03/19/2003]
Place each number from 1 through 10 in a box. Each box must contain a number that is the difference of two boxes above it, if there are two above it.

Pyramid Problem [9/1/1996]
You have a pyramid (1 circle on the top layer, 2 on the second, 3 on the third, 4 on the fourth) and you can only move three circles to turn it upside down...

Quickly Finding the Day of the Week [11/14/2000]
Today is November 14, 2000, a Tuesday. What day of the week was November 14, 1901?

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

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

Reversing the Digits [05/29/2003]
Finding pairs of two-digit numbers that yield the same product when you reverse their digits.

Russian Nim [02/15/1999]
Strategies for winning at Russian Nim (the "20" game).

Send More Money [05/12/1997]
Find the digit that each letter represents in the equation SEND + MORE = MONEY.

Sequence Question from IQ Test [06/28/2007]
Find the missing number in the sequence 11 > ? > 1045 > 10445.

Simultaneous Equations with Integral Solutions [11/29/1996]
What kind of a math project could I do with magic squares?

Six Lines, 4 Triangles [8/19/1996]
How can you form four triangles from six toothpicks?

Six Lines Make Twelve Triangles [11/06/2002]
How can I use 6 lines to make 12 triangles?

Skilled and Semi-Skilled Workers [09/04/2002]
Four skilled workers do a job in 5 days, and five semi-skilled workers do the same job in 6 days. How many days will it take for two skilled and one semi-skilled worker to do that job?

Solving a 3 x 3 Magic Square [09/29/2005]
There are mechanical methods to fill in Magic Squares, but here Dr. Wilko presents a nice way to reason out the solution of a 3 by 3 square.

Solving a Math Poem [05/24/2000]

Solving Problems by Making Organized Lists [04/09/2008]
To find 11 coins that total $1.37, Dr. Ian makes organized lists which reduce the problem to smaller and smaller problems until it can be solved. This general strategy is useful in many math problems.

Solving Questions [08/28/2002]
In a poll of 34 students, 16 felt confident solving quantitative comparison questions, 20 felt confident solving multiple choice questions.... How many students felt confident solving only multiple choice questions and no others?

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


Splitting a Clock Face into Desired Sums [11/14/2007]
Break a clock into exactly five pieces such that the sums of all the numbers on each piece are 8, 10, 12, 14 and 16.

Squares in a Square [01/23/2003]
If you have a 50x50 square with small squares inside it, how many squares will there be altogether?

Squares in Rectangle Formula [06/30/2003]

Squares on a Checkerboard [04/26/1998]
How many squares are there on a checkerboard?


Squaring Two-Digit Numbers Ending in 5 [09/10/2001]
Take the first digit, multiply it by the next consecutive number, and place it in front of 25. Can you prove this shortcut?

Stair Patterns [02/27/2001]

Subtraction Pattern for Roman Numerals [9/7/1995]
The question is, given that 4 is 'IV' and 9 is 'IX' and 900 is 'CM', does the subtraction pattern follow for two numerals more than two 'levels' apart, and can numerals which represent numbers starting with 5 be subtracted? For example, would 99 be 'IC', would 450 be 'LD', and would 995 be 'VM'?

Sum of Numbers 1-500 [06/20/2001]
What is the formula to find the sum of the numbers one to five hundred?

Sums Divisible by 11 [10/10/2001]



Sum Twice the Difference [10/18/2002]

Swimming Laps [04/15/2002]

Switching Dollars and Cents [10/07/1997]
How do I find an equation?

Tea and Cakes [11/13/2002]

Teaching Elementary Probability [10/07/1998]
If you toss a number cube 20 times, could it land on six 20 times?


Search the Dr. Math Library:

Search: entire archive just Middle School Puzzles

Find items containing (put spaces between keywords):
Click only once for faster results:


parts of words whole words

[Privacy Policy] [Terms of Use]


© 1994-2015 Drexel University. All rights reserved.