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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?
- Change for a Dollar [3/14/1995]
How many different ways can you make change for a dollar? Is there a
- Chessboard Squares [11/7/1994]
We discovered that there are 204 squares on a chessboard and found that you would add the different squares - 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64. Our teacher wants to know why it works and if there is a quick way to get the answer.
- How Many People? [06/11/2001]
There are three more people in front of Clancy than in front of Nancy,
and twice as many in front of Mary Ellen as in front of Nancy. The total
people in front of the girls is 11. How many people are in front of each
of the girls?
- Multiples of 9 Number Puzzle [03/23/2003]
If you take a two-digit number, add the digits, and subtract the sum
from the original number, why is the answer always a multiple of 9?
- The Polar Bear Club Question [3/17/1995]
I am looking for some information on a math game called Petals around the
- Rectangles and Factors [09/09/1998]
How many rectangles can you make with 10 small squares? 5 small squares?
12 small squares?
- Solving Number Sentences: A Strategy [07/11/2003]
I have been given a list of numbers without any plus or minus signs
and I have to place the signs between the digits.
- Sum of numbers and/or digits 1-100 [03/29/1997]
How would one go about adding up all the digits 1-100?
- Sum of Odd Numbers 1-50? [10/10/2001]
What is the sum of the first 50 odd numbers?
- Ways To List 1, 2, ... 10 Out of Order [02/25/1997]
How many ways are there to list the numbers one through ten so that no
number appears in its own position (i.e. 1 is not first in the list, 2 is
- 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.
- 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.
- 19 Odd Number Puzzle [10/22/2001]
What four odd numbers add up to 19?
- 25 Coins in a Dollar [05/07/2001]
Carlos has 25 coins whose total is $1.00. What are the coins?
- 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?
- 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
- 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.
- Arranging Toothpicks into Squares [10/22/2003]
How can I arrange 12 toothpicks to make 5 squares?
- 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
- Birthdate Puzzle [01/11/1998]
The problem starts: write the number of the month in which you were
born... it all works, but the teacher wants to know why.
- Bowling Pin Problem [02/17/2006]
Ten bowling pins are set up in the usual way forming a triangle with
the point facing the bowler. How can three pins be moved so that the
point now faces away from the bowler?
- Breaking One Big Problem into Several Smaller Ones [09/11/2003]
How can I change a dollar into exactly 26 coins?
- The Case of the 90 Apples [11/19/2002]
A Cadi gives 90 apples to three girls and says: you must sell these
apples in the market. Fatima, the eldest, takes 50, Cunda 30, and
Siha, the youngest, the remainder (10). If Fatima sells 7 apples for 1
dinar the others will sell their apples at the same price. The three
girls must sell all their apples and must get the same amount of
- Change for a Dollar [03/07/1999]
How many different ways are there to make a change for a dollar?
- Choosing 3 of 6 Colors [03/03/2000]
Patrick has a box of crayons with red, blue, yellow, orange, green and
purple. How many different ways can Patrick select 3 colors?
- Claim the Last Flag [10/25/2002]
Two teams face 21 flags. Teams take turns choosing 1, 2, or 3 flags at
each turn. The team that can claim the last flag wins.
- Clock Hands Perpendicular [10/15/2001]
What time of day is it when the hour hand is perpendicular to the minute
hand, and the minute hand points to the number 12?
- Combining Numbers [08/04/2002]
Combine the numbers 3, 3, 8, and 8, using only addition, subtraction,
multiplication, and division, to come up with the number 24.
- Comparing Sums of Odd and Even Integers [03/31/2004]
Which is greater, the sum of all of the even numbers that are less
than 100, or the sum of all of the odd numbers that are less than 100?
It takes too long to add them all up!
- Connect Nine Dots [11/4/1996]
Draw four lines connecting nine dots in a grid without lifting the pen
from the paper.
- Counting Days of the Week [02/02/1999]
If today is Thursday, what day would it be 120 days from now?
- Counting Seconds [12/13/2002]
Ali counted to 10, speaking a number every 5 seconds. How long did the
complete count take?
- Cutting a Cake into 8 Pieces with 3 Cuts [09/08/2002]
How do you cut a cake into 8 pieces making only 3 cuts? How do you cut
a doughnut into 12 pieces with only 3 cuts?
- Cutting Slits in a Piece of Paper [02/01/2002]
How can you cut a hole in a piece of paper so a person can go through it?
- Dividing a Clock into Three Equal Parts [10/27/2002]
Can you divide this clock into three parts using two lines and making
all of the parts add up to the same number?
- Duration of a Clock's Strike [01/21/2004]
If it takes seven seconds for a clock to strike 7 o'clock, then how long does it take to strike 10 o'clock?
- Eight Circles, Sum is 13 [09/25/2002]
Arrange the numbers 1,2,3,4,5,6,7,8 in a given pattern so that the sum
of the numbers in any line equals 13.