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?



Find Two Numbers [11/14/2001]
The sum of two numbers is 16 and their product is 48.

First 500 Even/Odd Numbers [03/14/2002]
Is there a formula for the answer to the difference of the sum of the first 500 even numbers and the sum of the first 500 odd numbers?


Five Dollars in Change [10/07/1997]
I need to make $5.00. I have to use 100 coins but I can't use nickels.

Five Lines Through Twelve Dots [11/07/2000]
I have a picture made of 12 dots in a 3x4 pattern. Without lifting my pencil, how can I draw five straight lines that pass through them all?

Forming a Regular Pentagon by Folding Paper [3/11/1996]
Is it possible to form a regular pentagon from a strip of paper of any size by just folding?

Formula for Easter [06/12/1999]

Formula for Squares inside Rectangles [06/29/2003]

Formula for the Day of the Week [05/21/1997]
Please tell us what day of the week the Declaration of Independence was signed on, and the formula to determine it.

Four 4's Puzzle [10/24/2001]
How can you get 73 by using 4 fours and any mathematical equation?

The Four Doors of Xanth [02/11/1998]
Each door conceals one item: a treasure, a rope, a key, and a lantern. You must find all four items in a particular order to keep the treasure.

Four Four's, 2-10 [11/24/1997]
Find a numerical expression using four 4s for each integer from 2 to 10.

Four Twos Puzzle [05/31/1999]
How can I get 15, 17, 19 and 21 using 4 twos?

Friday the 13ths in a Year [08/10/1999]
How can I figure out the maximum number of Friday the 13ths there are in one year?

Frogs Changing Sides [09/04/2002]
What is the least number of jumps needed for all the frogs to trade sides?

Fun Addition [8/21/1995]
Given the numbers 1 through 9, using each number only once, how many problems can be formed when adding two three-digit numbers? Is the sum of the digits in the sum always 18?

A Game in Three Rounds [04/19/1999]

Game of 24 [7/15/1996]
A student takes four numbers and combines them by addition, subtraction, multiplication, division, or a combination thereof to produce an answer of 24.

Getting All the Utilities to Each House [5/17/1995]
There are three houses and three different utilities. Can you connect each utility to each home WITHOUT crossing any lines?

The Gift of the Magi [09/08/2002]
What mathematical error can be found in the first paragraph of O. Henry's 'The Gift of the Magi'?

Girls and Coins [01/29/2001]
Five girls stopped for a soda on the way home from school. The girls were amazed to find that each of them had exactly six coins...


Grid Game [07/20/2001]

Guess and Check - How Many Coins? [10/03/2002]
Jeremy has seven fewer coins than Hanna. If together they have 83 coins, how many coins does Hanna have?

What's the only number system where half of five is four?

Heads and Legs [07/25/2001]

A Hen and a Half [09/23/1998]


Did you get his license number?

How Does the Crystal Ball Know What Number I Chose? [01/05/2010]
Doctor Ian reveals how a mind-reading crystal ball "knows" the number you've chosen: represent any two-digit number 'ab' as 10*a + b....

How Does the Fido Puzzle Work? [05/12/2004]
Can you give me the mathematical explanation of how the Fido puzzle works? You can find the puzzle at http://digicc.com/fido/.

How Heavy is the Brick? [11/15/1997]
If a brick weighs a kilogram plus half a brick, how heavy is the brick?


How Many Hidden Faces? [07/07/2002]

How Many Pencils? [09/05/2001]


How Much Money? [08/16/2001]
A man has 3 daughters, 4 sons, and a sum of money. If he divides the money equally among his daughters $2 will be left over...

How Old is Korinth? [09/09/1997]


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]


© 1994-2014 Drexel University. All rights reserved.