- Fraction Riddle - Joyce , 09/05/2003
How can 1/2 of 9 be 4?
- Freezer Roulette - Kev, 07/26/2002
Two people are trapped in a small freezer that is slowly getting
colder and colder... Is it possible for them to escape? If so, how?
What’s the maximum number of minutes required to escape given ANY
initial combination of button states?
- Friday the 13ths in a Year - Cole, 08/10/1999
How can I figure out the maximum number of Friday the 13ths there are in
- Frogs Changing Sides - Jean, 09/04/2002
What is the least number of jumps needed for all the frogs to trade
- Fun Addition - Horick, 8/21/1995
Given the numbers 1 through 9, using each number only once, how many problems can be formed when adding two three-digit numbers? Is the sum of the digits in the sum always 18?
- Fun Brain Twister - AQ, 8/22/1996
Use six 7's to write an expression that has a value of 110.
- A Game in Three Rounds - Razelene, 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 - Kurtz, 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 - Rosenbaum/Mahon, 3/14/1995
Using addition, subtraction, multiplication, and division, can you use
7,7,3,3 to make 24?
- A Geometry and a Logic Problem - Marsville, 3/11/1995
Problem 1: A cylindrical hole six inches long is drilled straight through
the center of a solid sphere. What is the volume remaining in the sphere?
Problem 2: The classical stay-switch problem.
- Geometry Puzzles - Creswell, 12/18/1995
A student asks Dr. Math for help in finding the correct combinations of
numbers to solve two puzzles.
- Getting All the Utilities to Each House - Borstein, 5/17/1995
There are three houses and three different utilities. Can you connect
each utility to each home WITHOUT crossing any lines?
- The Gift of the Magi - Cassie, 09/08/2002
What mathematical error can be found in the first paragraph of
O. Henry's 'The Gift of the Magi'?
- Girls and Coins - Shana, 01/29/2001
Five girls stopped for a soda on the way home from school. The girls were
amazed to find that each of them had exactly six coins...
- Giving Myself a Challenge - Stephanie, 09/20/2014
A student wonders if doing puzzles from math competitions would help her as she prepares for her advanced coursework. Doctor Ian suggests many ways to exercise lateral thinking skills, mathematical insight, and creativity in problem-solving no matter
- Grains of Wheat - Khalafalla, 07/14/1999
The person who invented the game of chess was said to have been offered
any payment he wanted... How much wheat did he receive?
- Grandfather Clock and 7-Second Chime - Cindy, 06/06/2002
If it takes a grandfather clock 7 seconds to chime 7 o'clock, how long
will it take the same clock to chime 10 o'clock?
- Grid Game - Chad, 07/20/2001
This game for two players is played on a rectangular grid with a fixed
number of rows and columns. Play begins in the bottom left-hand square...
- Guess and Check - Johnathan , 06/17/2002
The sum of two numbers is 15. The difference is 3. What is the
- Guess and Check - How Many Coins? - Christine , 10/03/2002
Jeremy has seven fewer coins than Hanna. If together they have 83
coins, how many coins does Hanna have?
- Guessing a Mystery Number - Akash, 05/23/2007
One person thinks of a natural number and the other person has to try
to guess it by asking questions. The one who knows the number will lie
once at some point, but otherwise be truthful in answering the
questions. What's the best algorithm for finding
- Half of Five is Four? - Don, 11/04/2004
What's the only number system where half of five is four?
- Handshake Problem Variant - Bixler, 07/08/1999
Five couples go to a party and start shaking hands. One of the men
shouts, "Stop! How many hands did you shake?" Every person gives a
- The Haybaler Problem: Reflections and Refinements - Anonymous , 10/05/2002
Given pairwise weights, a student and Doctor Greenie reflect on how to deduce
individual ones before a PhD follows up with several simplifying insights of his own.
- Heads and Legs - Joseph, 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?
- Headscratch Letter Puzzle - Ting, 01/25/2002
Use the numbers 0 to 9 for each letter once: G*B=HA, D*E=E, I*C=C, H*
- A Hen and a Half - Chase, 09/23/1998
If a hen and a half lays an egg and a half in a day and a half, how many
eggs will five hens lay in 6 days?
- Hidden Faces in a Set of Cubes - Roden, 10/04/2000
Can you give us a hint for a formula that will tell you the number of
hidden faces in an arrangement of a cubes if you know the number of
- Hit-and-Run Prime Number Problem - Charlie, 12/10/2002
Did you get his license number?
- Hole in a Sphere - Klein, 12/30/1996
When you bore a 6 inch cylindrical hole through the center of a sphere,
what is the volume of the remaining solid?
- How Does the Crystal Ball Know What Number I Chose? - Cheryl, 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? - Karen, 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? - Malligan, 11/15/1997
If a brick weighs a kilogram plus half a brick, how heavy is the brick?
- How Many Friday the 13ths - Smith, 9/12/1996
Is there a way to figure how many Friday the 13ths can occur in a given
- How Many Games Were Tied? - Laura, 06/07/1999
How many games are tied if each team receives 3 points for a win, 1 point
for a tie, and no points for a loss, and after 4 rounds the accumulated
points are: Lions 22, Tigers 19, Mounties 14, Royals 12?
- How Many Handshakes? - Kathy, 01/29/2001
There are 40 people in a room. They shake each other's hands once and
only once. How many handshakes are there altogether?
- How Many Hidden Faces? - Amy, 07/07/2002
When you place a number of cubes in a row on a surface, how many of the
faces can't be seen from any position? Is there a formula for this?
- How Many Pencils? - Thomas, 09/05/2001
How many pencils does Al have if all of them are blue except 2, all of
them are yellow except 2, and all of them are red except 2?
- How Many People Went on the Cruise? - Jessica, 12/03/2001
At the end of a special cruise, the employees could not remember the
total number of people who were on board. However, they had the following
data from the passenger list: 520 European females...
- How Much Money? - Jessica, 08/16/2001
A man has 3 daughters, 4 sons, and a sum of money. If he divides the
money equally among his daughters $2 will be left over...
- How Old is Korinth? - Phillips, 09/09/1997
Korinth is twice as old as Marin was when Korinth was as old as Marin is
now. Marin is 18.
- How to Create a 4 x 4 Magic Square - Bernard, 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 - Gary, 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?
- The Hundred Fowls - Yana, 09/29/2001
If a rooster is worth five coins, a hen three coins, and three chickens
together are worth one coin, how many roosters, hens, and chickens
totaling 100 can be bought for 100 coins?
- I am 5 digits long... - Ceste/Larioni, 12/16/1994
... I am divisible by 3 and 9, but not 6; my digits add up to 27...
- If 1/x+x=5, what does 1/x^2+x^2 equal? - Shawn, 08/16/2002
A complex and an easy solution to the problem.
- Impossible Word - Babler, 04/14/2001
What word comes out to 575,151 when you multiply together the values of
- Indefinite Series, Perfect Squares - Connie, 01/01/1998
Across the first row of an 11-column table are the numbers 1991, 1992,
1993, .... 2000, 2001.
- Jack is Older than Jill - Danielle, 11/16/2001
If you reverse the digits in Jack's age, you get Jill's age. The sum of
their ages equals 11 times the difference between them. Jack is older
than Jill. What are their ages?
- Jack & Jill Mind Teaser - Staley, 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