\$\$ CHANGE FOR A DOLLAR \$\$

by

Nicholas A Cluster

What is the largest amount of money, obviously in coins each less than one dollar, you can have and not be able to make change for a dollar?

Discussion

~Consider 3 quarters and 3 dimes. You have \$1.05, but you cannot make change for a dollar.

What combinations of coins will give the maximum?

Using the given example lets see if we can increase the amount of money we have and not be able to give an exact change for a dollar.

We know we canŐt add a quarter, because we all know what four quarters equal! Lets add a dime.  This gives a grand total of \$1.15 and we still canŐt give change for a dollar.

Lets see what happens if we add another dime. We get a grand total of \$1.25, but we can give change for a dollar. We would have five dimes and we could use two of our quarters to give change for a dollar.

Lets try to add a nickel to our \$1.15, giving us a grand total of \$1.20. But can we give change for a dollar? Absolutely! So we canŐt use a nickel.

What about pennies? We know we must have less than five, because anything higher will allow us to give change for a dollar.

However, if we add four pennies, we get a grand total of \$1.19 and we still canŐt give change for a dollar!