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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?
- Paper-Cutting Trick [01/24/2001]
Is there a way to cut a sheet of paper so as to make a hole big enough to
- Pentagon Puzzle [09/18/2002]
Write the numbers 1 through 10 so each side of the pentagon has a sum
- Planting Trees [08/13/2002]
I have to plant 10 trees in 5 rows with 4 trees in each row.
- Product of Terms of a Sequence [04/18/2003]
Find the product of the first 99 terms of the sequence 1/2, 2/3, 3/4,
- Puzzle with a Difference [03/19/2003]
Place each number from 1 through 10 in a box. Each box must contain a
number that is the difference of two boxes above it, if there are two
- Pyramid Problem [9/1/1996]
You have a pyramid (1 circle on the top layer, 2 on the second, 3 on the
third, 4 on the fourth) and you can only move three circles to turn it
- Reversing the Digits [05/29/2003]
Finding pairs of two-digit numbers that yield the same product
when you reverse their digits.
- Sequence Question from IQ Test [06/28/2007]
Find the missing number in the sequence 11 > ? > 1045 > 10445.
- Sideways Math [12/11/1994]
I am a 4th grader at Laurel School in San Mateo and I want to see if you
can solve this problem. One + One = Two
- Six Lines Make Twelve Triangles [11/06/2002]
How can I use 6 lines to make 12 triangles?
- Skilled and Semi-Skilled Workers [09/04/2002]
Four skilled workers do a job in 5 days, and five semi-skilled workers
do the same job in 6 days. How many days will it take for two skilled
and one semi-skilled worker to do that job?
- Solving Problems by Making Organized Lists [04/09/2008]
To find 11 coins that total $1.37, Dr. Ian makes organized lists which
reduce the problem to smaller and smaller problems until it can be
solved. This general strategy is useful in many math problems.
- Splitting a Clock Face into Desired Sums [11/14/2007]
Break a clock into exactly five pieces such that the sums of all the
numbers on each piece are 8, 10, 12, 14 and 16.
- Squares in a Square [01/23/2003]
If you have a 50x50 square with small squares inside it, how many
squares will there be altogether?
- Squares on a Checkerboard [04/26/1998]
How many squares are there on a checkerboard?
- Squaring Two-Digit Numbers Ending in 5 [09/10/2001]
Take the first digit, multiply it by the next consecutive number, and
place it in front of 25. Can you prove this shortcut?
- Sum of Numbers 1-500 [06/20/2001]
What is the formula to find the sum of the numbers one to five hundred?
- Teaching Elementary Probability [10/07/1998]
If you toss a number cube 20 times, could it land on six 20 times?
- Ten Card Arrangement Puzzle [10/04/2005]
Arrange ten cards numbered 1-10 in a pile. Turn over the top card,
then move the next card to the bottom of the pile. Turn over the new
top card and move the next card to the bottom of the pile. Continue
like this until all ten cards have been turned over. The challenge is
to arrange the pile so the cards are turned over in order from 1 to 10.
- Thinking Outside the Pen [09/28/2004]
How can you put 21 pigs in 4 pig pens and still have an odd number of
pigs in each pen?
- Three Cuts and Seven Pieces [01/18/1999]
Is there any way that you can cut a pie into seven pieces with just three
- Use 2,3,7,8 to Write Math Expressions from 1 - 50 [10/03/2004]
Using each of the digits 2,3,7,8 one time, and any math operations you
know, find expressions with values of 44 and 46. I have done from 1
to 50 except these last two numbers.
- Ways to Make 50 cents [8/29/1996]
How many ways can you make 50 cents?
- Ways to Make Change for $1.00 [10/02/1997]
Are there really 292 ways to make change for $1.00?
- What Number Am I? [02/04/2002]
If you double me and take away 4 you get 8.
- Where Do the Parentheses Go? [09/12/2003]
Add parentheses to 2 + 7^2 - 3^2 / 3^2 - 1 * 5 = 35 to make it a true
- 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...
- Why are Manholes Round? [8/26/1995]
Why is a manhole round?
- Wolf, Cabbage, Goat, and River [9/11/1996]
A man has a goat, a wolf and a cabbage. He must cross a river in a boat
that will only carry one item at a time...
- 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 that Equal $1 [09/02/1997]
Letters of the alphabet are given values: a = 1 cent, z = 26 cents.
- Write a Three-Digit Number [10/24/2001]
Write a three-digit number using the digits 3, 6, and 9. The hundreds
digit is the sum of the tens and ones digits. The ones digit is greater
than the tens digit.
- Writing Roman Numerals [9/7/1995]
A student asks how to write the numbers 7000 and 7659 in roman numerals.
- 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?