Question

Suppose that you work for a company that offers $25 and $60 gift certificates. Determine the money denominations that you can create using these denominations. Then use strong induction to prove your conjecture.

Answer 1

The money denominations that can be created for the $25 and $60 gift certificates are:

$5, $10, $20, and $50.

Explanation:

To give the $25 gift certificate to a worker, the company will give either two of $10 plus one of $5 denominations or one of $20 plus one of $5 denominations. These denominations will result in the same $25.

To give the $60 gift certificate to a worker, the company will either give one of $50 and one of $10 denominations, three of the $20 denominations, or six of the $10 denominations. These denominations in their different combinations will result in the same $60.