$$ CHANGE FOR A DOLLAR $$

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!