Ask Dr. Math

Middle School Archive

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?

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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 with?

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 repeated letters?

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?

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