See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Puzzles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to frequently posed puzzles:
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?
- Which Car is in the Pole Position? [08/14/1999]
Clues for finding starting positions of the 10 cars entered in the
Rithmetic Road Rally.
- Which Grasshopper Wins the Race? [06/11/2003]
The larger grasshopper covers 10 inches per jump, while the smaller
one covers 5 inches. The smaller grasshopper takes 2 jumps for every
jump of the larger grasshopper. Which one wins, and why?
- Who Finished In What Place? [12/15/2002]
Sarah, Carla, and Kim were the finalists at a gymnastics meet...
- Who Made Which Toys? [12/21/1998]
A math logic problem, from a rhyme describing Santa's toymakers.
- Why the Motionless Runner Parodox Fails [01/01/2005]
I read about the Motionless Runner paradox on your site, and I am now
convinced that motion is an illusion. Can you help me understand why
the paradox can't be true?
- Wilbert the Wonder Dog [11/14/2002]
Five masters and their five dogs need to cross a river.
- Wolves and Pens Puzzle [08/30/2005]
Nine wolves are in a square enclosure. Build two more square
enclosures and put each wolf in a pen by itself.
- Words Equal to a Dollar [10/11/2001]
I need one-dollar words: a = 1, b = 2, c = 3...z = 26. I would like a
list of words that equal 100.
- Words that Equal $1 [09/02/1997]
Letters of the alphabet are given values: a = 1 cent, z = 26 cents.
- Working Backward [11/30/1999]
A woman sells half of her eggs and half an egg to Peter. Later, she sells
half her eggs again and half an egg to John, and so on with more people.
Finally the woman is left with only one egg. How many eggs did she start
- Working Backward [01/22/2001]
Ann, Barry, Chip, Doug, Evelyn, and Fred went to lunch to celebrate
Evelyn's and Fred's birthdays... How much should each person pay?
- World War II Window Blackout [10/21/2001]
Mr. Brown had a square window 120cm x 120cm, but the only material he
could find was a sheet of plywood 160cm x 90cm; same area, different
shape. He drew some lines and cut out just two congruent shapes, which he
joined to make a square of the correct size. How did he do it?
- Write a Sum That Totals 100 Using Digits 1 - 9 [05/30/2004]
Is it possible to arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 so that when added they total 100? Only adding is permitted and the numbers can be rearranged. Each number can only be used once.
- Written Numbers [05/12/1997]
What is the biggest number that can be written (in English) without
- Zingers [11/05/2002]
What are zingers when referring to numbers? What determines whether
or not a number is a zinger?
- ZOTTFFSSE Puzzle [10/02/2002]
What comes next in this letter sequence: ZOTTFFSSE?