See also the
Dr. Math FAQ:
3D and higher
Browse Elementary Puzzles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to frequently posed puzzles:
A hen and a half...
Measuring with two containers.
Heads, legs: how many animals?
- Eleven Sections of Fence [05/29/2003]
I have a grid containing 16 squares. Each square represents 1 acre. I
need to draw 11 sections of fence along the dotted lines of the
squares so that 4 fields are formed, each containing 4 acres of land.
- Finding a Rule That Fits an Input-Output Problem [08/26/2006]
My daughter has an input-output chart problem where she has to find a
rule and fill in the missing numbers. How can I help her with it?
- Finding Input-Output Rules [10/08/2003]
My 3rd grader is having trouble finding rules to change one list of
numbers (the inputs) into another (the outputs)...
- Finding the Bad Machine by Gumball Weight [05/13/2008]
Nine gum ball machines produce gum balls that weigh 1 ounce, and one
bad machine produces identical looking balls that weigh 0.5 ounce.
With one weighing on a scale, determine which machine is defective.
- Finding the Next Number in a Series [07/22/2002]
Are there any formal or systematic methods for solving problems that
ask you to find the next number in a series?
- Find Two Numbers [11/14/2001]
The sum of two numbers is 16 and their product is 48.
- Four Twos Puzzle [05/31/1999]
How can I get 15, 17, 19 and 21 using 4 twos?
- Fraction Puzzle Using Digits from 0 to 9 [02/04/2008]
Using all ten digits from 0 to 9 one time each, make five fractions
that have values less than 1/2.
- Fraction Riddle [09/05/2003]
How can 1/2 of 9 be 4?
- Fun Brain Twister [8/22/1996]
Use six 7's to write an expression that has a value of 110.
- A Game in Three Rounds [04/19/1999]
After three rounds each of the girls has 8 chips. How many chips did they
have at the start?
- 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
- The Game of 24 [3/14/1995]
Using addition, subtraction, multiplication, and division, can you use
7,7,3,3 to make 24?
- 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'?
- 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?
- Heads and Legs [07/25/2001]
Joe counts 48 heads and 134 legs among the chickens and dogs on his farm.
How many dogs and how many chickens does he have?
- 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 to Create a 4 x 4 Magic Square [01/28/2004]
Is there a general technique for creating a 4 x 4 magic square so that
the rows, columns, diagonals, four center squares and four outside
corner squares each add up to a desired number?
- How to Make a Square with Three Lines [06/19/2001]
My teacher says it is possible to make a square with three lines, but I
don't know how to do it. Can you help me?
- I am 5 digits long... [12/16/1994]
... I am divisible by 3 and 9, but not 6; my digits add up to 27...
- Jack & Jill Mind Teaser [8/29/1995]
If Jack had a 5 gal. bucket and Jill had 3 gal. bucket, and they each
carried an equal amount to fill an 8 gal. bucket, how was this
- Kindergarten Math Problems [11/1/1994]
I am a kindergarten teacher who has some very interested and interesting
math students. Are you willing to talk with us about math? Maybe you have
a problem for us to work on so we can get acquainted?
- Longest Roman Numeral [05/03/2007]
Which year in our recorded history has had the greatest number of
Roman numerals in it?
- Magic Triangle Sums [02/04/2003]
Find 6 consecutive odd numbers such that their magic triangle sum is
25. Find 6 consecutive numbers such their magic triangle sum is 4.
- Making a Hard Square Sum Problem Easier [01/30/2004]
Given these eight numbers: 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, 1 3/4, and
2, place three numbers along each side of a square so that the sum of
the three numbers on each side of the square is equal to 3. Is there
a trick to doing this kind of problem?
- Making a Parallelogram [06/19/2001]
Make five shapes - a parallelogram, a square, and three triangles - into
- Making Change [04/15/1999]
What is the greatest amount of money John can have in his pocket?
- Math Riddle [03/12/2001]
How do 5 and 9 more make 2?
- Math Trick Question [02/02/2005]
How do I draw a square using only 3 lines?
- Multiplying by 11 [09/16/1997]
We said: 568 x 11 and after about 5 seconds she said the answer was 6248.
How did she do it so quickly?
- Multi-Step Patterns [09/04/2003]
Find the rule that will give the second number if you know the first...
- Number Puzzle: 26, 70 [09/12/2001]
The sum of two numbers is 26; 4 times the first number plus 2 times the
second number equals 70. What are the two numbers?
- Number Puzzle Based on Multiplication Ideas [08/07/2005]
Find the smallest possible natural number that ends in 6 such that if
the 6 is erased and placed in front of the remaining digits, the
resulting number is 4 times as large as the original number.
- Number Puzzle with Digits 1-9 in a 3 by 3 Grid [10/09/2006]
In a 3 cell by 3 cell grid, use the digits 1 through 9 to fill in the
cells so each horizontal, vertical, and diagonal row of three has a
sum of 15. I've tried many possibilities with no luck!
- Numbers on a Star Brain Teaser [01/03/2008]
Place the numbers 20, 21, 22, 23, 24, 25, 27, 28, 29 and 31 on a star
so that each line of four numbers has a sum of 100. Each number can
only be used once. Is there a way to do this besides guessing and
- One Billion as Product of Two Numbers with No Zeros [12/12/2001]
Write 1,000,000,000 as the product of two numbers, neither of which
contains any zeros.
- One Box of Eight Digits, Four Sums of Twelve [02/19/2014]
An adult struggles to arrange digits in a magic square-like array. Doctor Peterson
picks up on her insight about the pairs of smaller digits that combine with 8 to add up
to 12, extends her thinking, and proposes a strategy before compiling a selection of
similar puzzles and problem-solving methods.
- Order of Operations Problems - a General Strategy [10/23/2002]
Make equations using 7, 26, 46, and 15 to equal 160; 18, 9, 24, and 20
to equal 18.