## Ken's POTW

Change for a Dollar
1. 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.

2. 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)?

3. 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.

Source: 1. David Berthold. 2,3. Many sources.

Solution
Mail to Ken