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Browse Middle School Puzzles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to frequently posed puzzles:
Letter+number puzzles.
Number sentences.
Remainder/divisibility puzzles.
1000 lockers.
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?
 More Monkeys and Nuts [06/07/1999]

How can I solve this variation on the monkeys and the nuts puzzle?
 Multiples of Four [10/22/2001]

How many multiples of four from 1 through 1000 do not contain any of the
digits 6, 7, 8, 9, or 0?
 Multiplying/Adding Fractions Gives Same Answer [03/01/2002]

Find two fractions which, when multiplied and added, give the same
answer.
 Multiplying a Number by 4 [01/11/1999]

Can you help me find a few numbers that when you multiply them by 4, you
will get the original number backwards?
 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?
 Multiply Two Numbers (No Zeros) to make 5 Billion [01/05/2002]

What two numbers, neither of them containing zeros, can be multiplied
together to make 5,000,000,000?
 MultiStep Patterns [09/04/2003]

Find the rule that will give the second number if you know the first...
 Nine Digits, Perfect Squares  and Better Strategies [03/07/2010]

A puzzle about square numbers and the digits {1, 2, 3, ... , 9} leads
to an insight about problemsolving approaches in general.
 Number and Its Square Using All 9 Digits Exactly Once [05/22/1998]

Using multiplication facts to find all the whole numbers for which the
number and its square together use exactly nine digits 1, 2, 3, ..., 9
only once.
 Number Problem to Find Maximum Possible Product [02/01/2005]

Use each digit from 1 to 9 once to form two numbers such that their
product is maximized. For example, the numbers could be 1234 and 56789.
 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 19 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!
 Number Riddle [1/23/1996]

What am I?: 1 is 10 cents, 14 is 20 cents, 123 is 30 cents, 943 is 30
cents
 Numbers from Numbers [04/26/1997]

How do you get the number 87 only using the number 1994?
 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
checking?
 Number Strings and Reversing Numbers [02/20/2004]

I need to find an 18digit number in which no two consecutive digits
are alike and the number is such that it reverses itself upon being
multiplied by 4.
 Numbers with 5 Factors [02/06/2002]

I know that 16 has 5 factors (1,2,4,8,16). What other two numbers might
have 5 factors?
 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 Chicken, One Day [04/19/2002]

If a chicken and a half lays an egg and a half in a day and a half,
how many eggs can one chicken lay in one day?
 On or Off? [05/26/2001]

How can I determine whether an automatic sprinkler system is on or off at
3:30 A.M., based on timed observations by the night watchman?
 The Orbit of Mercury [9/6/1995]

The number of days it takes Mercury to revolve around the sun is a
palindrome. Each digit is a cube greater than one. How many days does it
take Mercury to complete its orbit?
 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.
 Painting Half a Room Each Day [03/20/2002]

If Bob paints half of a room one day and decides to keep painting half
each day, why is the answer infinite?
 Palindromes [02/24/1998]

Two 4digit palindromes are added to give a 5digit palindrome N. What
are the possible numbers for N?
 PaperCutting Trick [01/24/2001]

Is there a way to cut a sheet of paper so as to make a hole big enough to
walk through?
 Pascal's Triangle Game [03/23/2001]

How could I make a game using Pascal's triangle?
 Passing Ships [05/12/1999]

Every day a ship leaves San Francisco for Tokyo... How many Tokyo ships
will each San Francisco ship meet?
 Paths Walked, Worked Backwards [01/03/2014]

Without counting them all, how would you enumerate the number of southeasterly
paths the insect could walk along the rectangular grid? Doctor Peterson recaps
approaches from elsewhere in the archives before pursuing a more efficient enumeration strategy.
 Pentagon Puzzle [9/12/1996]

Three numbers are placed on each side of a five sided pentagon with the
numbers on the corners being used on two sides...
 Pentagon Puzzle [09/18/2002]

Write the numbers 1 through 10 so each side of the pentagon has a sum
of 14.
 Perilous PingPong [11/14/1997]

Weigh the balls to find the one that's different...
 The Perils of Predicting Patterns [11/02/2003]

What comes next in 1,3,6,10 ___? Is it 12 or 15?
 The Pharaoh's Will [05/16/2000]

As he lay dying, the Pharaoh proclaimed: "I bequeath 1/3 of my estate to
my oldest child; 1/4 of my estate to the next oldest child; and to each
succeeding child, except the youngest, the next unit fraction of my
estate; and to the youngest the remainder."
 Placing Coins in a 5x5 Matrix [04/25/2000]

Each of 5 rows and colums in a grid row and column should equal a
specific dollar amount: we must place 5 halfdollars, 5 quarters, 5
dimes, 5 nickels and 5 pennies in the grid...
 Placing Coins That Touch [8/7/1996]

How many 20cent coins can you put around a 20cent coin so that all of
them touch?
 Planting Trees [08/13/2002]

I have to plant 10 trees in 5 rows with 4 trees in each row.
 The Predetermined Sum Puzzle [02/02/2001]

I pick 5 digits, and write them down. My friend tells me a sum. Then I
pick 5 more digits, he picks 5, I pick 5, and he picks 5. The sum he told
me is the sum of all 5 lines. How did he know what it would be?
 Price of House, Commission [8/29/1996]

If a real estate agent recieves 6 percent of the selling price of each
house she sells, then what should be the sale price of a house if a
seller wants to keep $61,000?
 Prices in Store 88 [07/05/1999]

In Store 88 they sell exactly ten items, some items with the same price
as others, but the only the digit on the price tags of each item is 8...
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