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?
- Find the Heavier Coin of 12 in 3 Weighings [11/17/1996]
If there are twelve coins in a bag, one of which is either lighter or
heavier than the others, find the fake coin in exactly 3 weighings AND
determine if it is lighter or heavier than the others.
- Find the Pattern, Complete the Combinations [01/13/2002]
Find the pattern: 3*4=5, 8*4=0, 3*7=2, 1*2=9, and use it to complete the
combinations: 5*5=?, 4*4=?, 5*7=?
- Find Two Numbers [11/14/2001]
The sum of two numbers is 16 and their product is 48.
- First 500 Even/Odd Numbers [03/14/2002]
Is there a formula for the answer to the difference of the sum of the
first 500 even numbers and the sum of the first 500 odd numbers?
- The 'First to 100' Game [03/12/2001]
Two players take turns choosing any number from 1-10, keeping a running
sum of all the numbers. The first player to make this sum exactly 100 is
the winner. Is there a surefire way to win this game?
- Five Dollars in Change [10/07/1997]
I need to make $5.00. I have to use 100 coins but I can't use nickels.
- Five Lines Through Twelve Dots [11/07/2000]
I have a picture made of 12 dots in a 3x4 pattern. Without lifting my
pencil, how can I draw five straight lines that pass through them all?
- Forming a Regular Pentagon by Folding Paper [3/11/1996]
Is it possible to form a regular pentagon from a strip of paper of any
size by just folding?
- Formula for Easter [06/12/1999]
Is there a formula for finding the month and the day on which Easter
falls in a given year?
- Formula for Squares inside Rectangles [06/29/2003]
Is there an equation for how many squares there are in a rectangle
divided up into 1cm blocks?
- Formula for the Day of the Week [05/21/1997]
Please tell us what day of the week the Declaration of Independence was
signed on, and the formula to determine it.
- Four 4's Puzzle [10/24/2001]
How can you get 73 by using 4 fours and any mathematical equation?
- The Four Doors of Xanth [02/11/1998]
Each door conceals one item: a treasure, a rope, a key, and a lantern.
You must find all four items in a particular order to keep the treasure.
- Four Four's, 2-10 [11/24/1997]
Find a numerical expression using four 4s for each integer from 2 to 10.
- Four Twos Puzzle [05/31/1999]
How can I get 15, 17, 19 and 21 using 4 twos?
- Friday the 13ths in a Year [08/10/1999]
How can I figure out the maximum number of Friday the 13ths there are in
- Frogs Changing Sides [09/04/2002]
What is the least number of jumps needed for all the frogs to trade
- Fun Addition [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?
- 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
- Getting All the Utilities to Each House [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 [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 [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...
- Grandfather Clock and 7-Second Chime [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 [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 - 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?
- Half of Five is Four? [11/04/2004]
What's the only number system where half of five is four?
- 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?
- A Hen and a Half [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 [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 [12/10/2002]
Did you get his license number?
- 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 Many Games Were Tied? [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 Hidden Faces? [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? [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? [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? [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? [09/09/1997]
Korinth is twice as old as Marin was when Korinth was as old as Marin is
now. Marin is 18.