Pocket Change

Did you know that you can have $1.19 in pocket change and not be able to provide $1.00 in change?

How can you have more than $1.00 but not be able to produce a dollar’s worth in change?

Very simple – no nickels!

Three quarters, four dimes and four pennies equals $1.19. This combination of change also equals the largest set of coins that won’t make a $1.00 in change. The closest you can get with this combination is $.99 on the low side or $1.05 on the high side of $1.00.

Let’s see: three quarters, two dimes and four pennies equal the $.99 with two dimes left over. Or, three quarters and three dimes equal the $1.05 with a dime and four pennies remaining.

Or, taking the half dollar as part of the coinage, one half dollar, one quarter, four dimes and four pennies would yield similar results.

But, what happens when you introduce a nickel to the mix? What is the largest combination that won’t provide change for a $1.00?

How about four pennies, two nickels, one dime and three quarters for $.99. If you add any one of the coins, you will be able to make $1.00 in change.

Now, let’s add the half dollar. With four pennies, two nickels, one dime, one quarter and one half dollar, you will have $.99.  Again, adding any one coin yields the ability to make $1.00 in change.

So, quiz your friends. Ask them to give you the largest total money and a corresponding combination of coins that won’t yield change for a $1.00.