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A wealthy king divided his riches between his three sons. He said, "I have 21
identical, equally large chests - seven of them are completely filled with gold coins,
seven are half-filled with gold coins, and seven are empty. Can you divide these 21 chests
among yourselves without taking the gold coins out of them, so that you all have the same
number of gold coins and the same number of chests?"
There are two possible solutions. What are they?
1. What is the largest amount of money you can have in $1, $2, $5, $10, $50 bills and still not be able to make exact change for a $100 bill?
2. How much money (the most) can you have in pennies, dimes, nickels, and quarters and still not be able to make exact change for one dollar?
3. How many possible ways are there to make $1.00 out of coins (including the dollar piece and .50 cent pieces)? Assume that "3 x 25c plus 25 x 1c" only counts as one solution, no matter what order the coins come in.
4. How much money can you have if you had coins of 1, 2, 5, 10, 25, and 50 cents and still not be able to make exact change for one dollar?
5. British coins under £1 are 50p, 20p, 10p, 5p, 2p and 1p. Applying the same puzzle to Britain, what is largest amount of money that will not make change for a pound?
6. One day, John Flynn was walking down the street and a man walked up to him. The man asked, "Do you have change for a dollar?". John reached into his pocket and took out his change purse, where he kept all of his coins. Inside of the change purse he had an even number of coins totalling $7.50, and all of them U.S. issue. John told the man truthfully, "I'm sorry, but I don't have change for a dollar.". What were the coins in John's change purse?
A dealer has 1000 coins and only 10 money bags. He has to divide the coins over the ten bags so that he can make any number of coins simply by handing over a few bags. How must he divide the money over the ten money bags?
Ten coins, numbered 1 to 10, lie in a straight line on the table.
The aim is to make five piles of two coins in five moves. But each coin may jump over two coins only and then land on the third. The coins may jump in both directions. Do you know how?
You have three cups and eleven coins. Try to divide the coins over the three cups so
that there is an odd number of coins in each cup. That was easy. Now you only have 10
coins. Can you still do it? It is possible - there are 15 different solutions to this
puzzle. Can you find all 15?
1. Draw ten circles and start with the
coins cycling quarter, dime, nickel, penny as follows:
2. Same as the above puzzle, except add a third empty circle on the right side
Your goal is to make exactly five dollars ($5.00) using exactly 100 coins. Each coin
must be either a dollar ($1.00), half dollar ($0.50), quarter ($0.25), dime ($0.10), or
How many _different_ piles of coins can be made to fit these criteria?
Suppose I place a penny and a quarter on the table, and make you the following offer:
If you make a true statement, I will give you one of the coins.
If you make a false statement, I will give you neither coin.
What statement can you make that will force me to give you the quarter? Explain your answer.
You are blindfolded and in front of you is a pile of 12 coins. You are allowed to touch the coins, but can't tell which way up they are by feel. You are told that there are 6 coins head up, and 6 coins tails up but not which ones are which. How do you make two piles of coins each with the same number of heads up?
You have fifty coins, one of which is heavier or lighter than the others. You have a balance that doesn't tell you how heavy each coin is. You can only use the balance three times. How can you identify the odd coin?
How many ways can you make (US) 50 cents without cents?