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Browse High School Puzzles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to frequently posed puzzles:
1000 lockers.
Letter+number puzzles.
Getting across the river.
How many handshakes?
Last one at the table.
Monkeys dividing coconuts.
Remainder/divisibility puzzles.
Squares in a checkerboard.
Weighing a counterfeit coin.
What color is my hat?
 Magic Triangle, 2 Numbers/Side [04/25/2003]

Natural numbers can be placed in an arrangement so that the sum of 3
numbers on each side of a triangle is always the same. Is it possible
to find a magic triangle with 2 numbers?
 Magic Wheel [03/20/2002]

Given a wheel with 16 spokes and a hub, enter the whole numbers 117 in
the hub and at the end of spokes. The sums of the 3 numbers along the
spokes must be equal.
 Make 24 [01/03/2003]

We have to make 24 by using 1, 3, 4, and 6.
 Make $5 Using One of Each Coin [07/07/2001]

You have 100 coins: pennies, nickels, dimes, quarters, and half dollars.
Use at least one of each to add up to $5.00.
 Make 7,7,3,3 into 24 Using +  * and / [02/12/2002]

Make the numbers 7,7,3,3 equal 24 using the operations addition,
subtraction, multiplication, and division.
 Making $5 Using 50 Coins [12/02/2005]

How many ways can you make $5 with 50 coins and without using dimes?
 Making a Magic Square [7/4/1996]

How do you make a magic square?
 Making Change for a Dollar [05/29/2001]

What is the smallest number of coins you CANNOT make change with?
 Mangoes at the Gates [04/06/2001]

To pick some mangoes from a tree inside seven walls with seven guards,
you tell each guard that you'll give him half of the mangos you have, but
he must give you back one mango. What's the minimum number of mangos you
must pick to have at least one mango left?
 Math Puzzle: Day of the Week [02/04/1998]

Why does the following math problem work, irrespective of the number you
use 07 for the day of the week?
 Maximizing Output of a Restricted Function [11/1/1996]

Create a function whose domain is restricted to complex numbers but whose
range is real, that is, nonconstant, has no constant term, and contains
no number greater than 3.
 McNuggets [03/10/2002]

At one McDonald's location, McNuggets come in boxes of 6, 9, and 20. What
would be the largest number of McNuggets that you could not buy?
 Milk Bottle Puzzle [09/24/2001]

Given 18 milk bottles and a milk crate 6 holes wide by 4 holes deep, put
an even number of bottles into every row and column.
 Million Point Word Puzzle [05/18/2005]

If a = 1, b = 2, ... , z = 26, is there a word that when the values of
the letters are multiplied will make a product of one million?
 Millionth Digit of the Counting Numbers [02/26/2001]

A number is formed by writing the counting numbers in order:
123456789101112131415... What is the one millionth digit in this number?
 Minesweeper Puzzle [10/24/2001]

For the general case of an MxM board with N bombs, can you find the
maximum value of the sum of all the numbers that are not bombs?
 Minimum Number of Cuts to Slay the Dragon? [01/14/2007]

A magic dragon has 3 heads and 3 tails. A knight with a magic sword
can make four types of cutsone head, two heads, one tail, or two
tails. For each type of cut, the dragon regrows one head, nothing,
two tails, or one head respectively. The knight must remove all
heads and tails to slay the dragon. What's the fewest number of cuts
he can make?
 Minimum Number of Trips [07/01/2001]

A fully laden lorry can carry fuel and supplies for a trip into the
desert of up to 400 miles... How many trips would be needed to penetrate
600 miles and back?
 Minimum Set of Weights Puzzle [10/18/2001]

What is the minimum number of weights needed for a scale that can weigh
objects from 1100 pounds, inclusive, at onepound increments?
 Money Puzzle [01/05/1998]

A man goes to the bank and asks for x dollars and y cents.
 Monkeys, Coconuts, and Seven Piles [11/29/2001]

Seven monkeys spend the day gathering coconuts. As night falls, they
gather all the coconuts into one pile and agree to divide them up evenly
in the morning. At 12:00pm one monkey gets up and divides the pile of
coconuts into seven piles with one left over...
 Monkeys in the Jungle [11/18/1996]

How can a group of hungry monkeys carry the bananas to their friends
across the jungle? They want to arrive with the maximum number uneaten.
 More Monkeys and Nuts [06/07/1999]

How can I solve this variation on the monkeys and the nuts puzzle?
 Moving Knights on a Chessboard [01/27/1999]

Given 4 knights at the 4 corners of a 3by3 chessboard, can the knights
exchange places if they can move only in the following way?
 Multiplication Using +, , and 1/x [10/25/2000]

Suppose you had a calculator with only the +, , and 1/x operator
buttons. Could you do multiplication with it?
 Multiplying/Adding Fractions Gives Same Answer [03/01/2002]

Find two fractions which, when multiplied and added, give the same
answer.
 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?
 New School Lockers [01/28/2001]

Which locker was touched the most?
 Nim [09/26/2000]

What is the principle of Nim and what is its application?
 Nonnegative Integers [11/15/2001]

How many nonnegative integers consisting of 13 digits are divisible by
5? How many nonnegative integers consisting of 13 different digits are
divisible by 5?
 No Two Consecutive Terms Divisible by 2 or 3 [10/13/2002]

In how many ways can numbers in the set {1,2,3,4,5,6} be ordered so
that no two consecutive terms have a sum that is divisible by 2 or 3?
 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.
 The Number of Possible Sudoku Puzzles [03/04/2006]

I calculated that there are 16,930,529,280 different possible Sudoku
puzzles, but an article I saw said that there are many more. How many
are there, and how would you determine it?
 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 [02/12/1997]

Find a 9digit number in which the 1st digit is the number of 0's, the
2nd digit is the number of 1's..., and the 9th digit is the number of
8's.
 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 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?
 Opening and Closing 1000 Lockers [03/16/1997]

There are 1000 closed lockers and 1000 students. The first student opens
every locker; the second student reverses every other locker...
 Pascal Calendar Program [02/12/2002]

Holiday homework: make a program in Pascal that with a date of our choice
give us the day of the week.
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