I went into the bank to get change for a dollar. The teller said, "How do you want the change, buddy? I mean, there are 292 ways involving pennies, nickels, dimes, quarters, and half-dollars to give change for a dollar!"

Since I didn't like her attitude, I didn't answer her question. I simply said, "Well, I certainly don't want any pennies."

How many ways are there for her to give me change now?

(Note: Americans, always shunning simplicity have chosen to name their coins in the following easy-to-remember manner: Penny=1 cent, Nickel=5 cents, Dime=10 cents, Quarter=25 cents, Half Dollar=50 cents)

We just have to find as many ways to make 100 with 5, 10, 25 and 50. There are:
50 + 50
50 + 25 + 25
50 + 25 + 10 + 10 + 5
50 + 25 + 10 + 5 + 5 + 5
50 + 25 + 5 5's
50 + 5 10's
50 + 4 10's + 2 5's
50 + 3 10's + 4 5's
50 + 2 10's + 6 5's
50 + 10 + 8 5's
50 + 10 5's

That is eleven ways, so there are 11 ways to make 100 from those coins. We can find more ways by replacing 50 with one of the other ways, but each time there is one less way. So the amount of ways is 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66.

I confused myself, so this might be wrong :)

Posted by Lewis on 2003-06-18 07:06:19