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?
- 1000 $1 Bills in 10 Envelopes [12/11/2002]
Put 1000 $1 bills into 10 envelopes in such a way that someone can ask
you for any amount of money from $1 to $1000 and you can give it to
him through a combination of the envelopes.
- 1000 Lockers [11/06/1997]
The 1st student opens all 1000 lockers, the 2nd student closes lockers
2,4,6,8,10, etc., the 3rd student opens lockers closed and closes lockers
open on lockers 3,6,9,12,15...
- 10 Digit Number Puzzle [09/14/2004]
Write a 10 digit number where the first digit tells you the number of
zeros in the 10 digit number, the second digit is the number of ones
in the number, the third digit is the number of twos in the number and
so on until the 10th digit is the number of nines in the number.
- 10 Square Units on Dot Paper [03/01/2003]
How can I draw a square with 10 square units on dot paper?
- 121, 111211, 311221 Puzzle (Look and Say Sequence) [10/23/2001]
121, 111211, 311221 - what's the next number?
- 1 2 3 4 5 6 7 8 9 0 = 100 [01/24/2002]
Leave the numerals in this order. Place only addition and subtraction
signs to make it a true statement.
- 12345679 Puzzle - The Missing Eight [08/17/2001]
Start with 12345679 and pick a number...
- 16 Squares and 5 Colors [08/15/2002]
You have 16 squares in a box, with 5 colors: 4 blue, 3 green, 3 red, 3
white, and 3 black. The same colors can't touch or be in the same row.
- 1, 7, 23, 55, 109, 191, ___ [10/03/2002]
My family is stumped on this number pattern: 1,7,23,55,109,191,___ ...
- 174 Game [08/16/2001]
Players announce numbers (1-8) in turn. The judge adds the numbers they
announce. If the sum becomes 174 or more, that player wins. In order to
win the game, which number should be given first?
- 19 Apple Trees [06/29/2001]
You have 19 apple trees. How could you place them in 9 rows of 5?
- 19 Odd Number Puzzle [10/22/2001]
What four odd numbers add up to 19?
- The 22 Puzzle [03/12/2002]
Choose three different digits from 1-9, make all the 2-digit numbers you
can from these 3 digits... why is the answer always 22?
- 25 Coins in a Dollar [05/07/2001]
Carlos has 25 coins whose total is $1.00. What are the coins?
- 25 Coins in a Dollar [08/16/2001]
How can you get a dollar using 25 coins? Find five combinations.
- 300 Foul Shots [07/11/2001]
A basketball player shoots 100 foul shots on a given day, and increases
the number he shoots by 10 per day...
- 30th of the Month [06/18/2001]
What day does the 30th of the month most often fall on?
- 3 Digits Plus 3 Digits [12/09/2001]
Use the digits 1 to 9 only once in a sum that must be a three-digit
number plus another three-digit number to equal another three-digit
number. Each digit can only be used once, but all must be used.
- 3 Weighings Problem [12/09/1997]
You have a balance scale and 12 balls that all look and weigh the same
- 55 Cents, Seven Coins [05/15/2001]
How can you get 55 cents with seven coins (quarters, dimes, nickels or
pennies only) eight ways?
- 60 Eyes and 86 Feet [09/30/1997]
How many camels and ostriches were in the zoo?
- 8549176320 Puzzle [04/30/2002]
The following number is formed by a special pattern and is the only
one of its kind: 8549176320. What is the pattern?
- ABCD * 4 = DCBA [05/23/2000]
Find digits A, B, C, and D that solve the cryptarithm ABCD * 4 = DCBA.
- ABCDC - BEAAC = BADAD [03/25/2002]
What do the letters stand for if D = 0?
- ABCDE/4 = EDCBA [06/30/2003]
Find a five-digit number that, when it is quartered, gives an answer
which is its digits in reverse order.
- A,B,C,D Letter Puzzle [08/30/2002]
Place the letters A,B,C,D in the chart so that no letter appears twice
in any new row, column, or diagonal.
- ABCD x 4 = DCBA [08/22/1997]
What are the values of A,B,C and D? The values are between 0-9 and each
- Ages 27-30 Puzzle [11/06/2001]
Alan was 27 years old the day before yesterday. Next year he will be 30.
How is this possible?
- Alien Fingers and Bases [12/07/1998]
Scientists observe a class of young aliens through a telescope. These
equations are on their blackboard: 13 + 15 = 31, ... How many fingers do
the aliens have?
- Almost a Magic Square [12/16/1996]
Given a set of 16 numbers, place them in a 4 by 4 square so that the sum
of the members of each row or column equals 44.
- Apple Paradox [03/07/2002]
Ms. G and Mr. S each bring 30 apples to sell at the market...
- Area of the Tilted Quadrilateral within the Square [03/11/2013]
Given a unit square, construct one segment from each vertex to an opposite midpoint
so that pairs of these diagonals run parallel and intersect to form a quadrilateral. What
is the area of this shape?
- Arithmetic Code [05/09/1999]
Break the code, given that each of the following is true in ordinary base
- Arranging Numbers [06/26/2002]
Arrange the numbers 1-8 into the given configuration such that
consecutive numbers are never adjacent.
- Arranging Rose Bushes [9/13/1995]
A gardener laying out a rosebed found she could plant 7 rose bushes in
such a way that they formed 6 straight lines with 3 rose bushes in each
line. How was this possible?
- Arranging Toothpicks into Squares [10/22/2003]
How can I arrange 12 toothpicks to make 5 squares?
- Averaging 30 Miles Per Hour [03/17/1997]
If for half the distance of a trip you travel at 15 mph, what will your
speed have to be for the rest of the trip for you to average 30 mph?
- Bachet's Theorem [10/08/1998]
My maths teacher said that a mathematician discovered that you can make
any number by adding together a combination of no more than 4 square
- Balls and Boxes [9/1/1996]
How can you can place 21 balls in 4 boxes to have an odd number of balls
in each box?
- Ben and Bill [12/21/1997]
Bill + Ben's age = 91. Bill is twice as old as Ben was when Bill was as
old as Ben is now.