You have a half-dollar, a quarter, a dime and a nickel in your pocket. At a flea market you see some things you like and ask the vendor how much they cost. The vendor asks how much money you have and then shows you only pieces whose price matches exactly a combination of the coins in your pocket. What is the largest number of items the vendor can show you?
Solution
Try different possibilities. With 4 coins there are combinations of your four coins. (The empty combination doesn't count. Nothing is for free.) The question is whether some of these combinations come out the same--that is, for some given item there is more than one way to pay for it.