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 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.

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

Solution

Mail to Ken