What is the smallest number of coins that cannot make change for a
dollar? Each coin may be selected to be a silver dollar, half dollar,
quarter, dime, nickel, or penny. Examples:
1 coin
silver dollar
2 coins
2 halves
3 coins
half, 2 quarters
4 coins
4 quarters
5 coins
half, quarter, 2 dimes, nickel
6 coins
3 quarters, 2 dimes, nickel
or
half, 5 dimes
etc.
If all you hold are coins of the above possible denominations,
what is the largest amount of money you could have and not be able to
make exactly one dollar ($1.00)?
In how many ways can you make change for a dollar using only coins?
(For example: four quarters, OR ten dimes, OR nine dimes and two nickels,
OR ...)
Can you first show how many ways you can make change for
lower multiples of 5 cents?
Is there an iterative or combinatorial solution? (i.e. Can you
use the results of 50 cents and 25 cents to determine the result
for 75 cents?)
If you use a computer program, please send it, as well as a simple
description of its operation.