Change for a Dollar
- 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
- 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,
- 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.
1. David Berthold.
2,3. Many sources.
Mail to Ken