There is a class of problems called "bar bets" where you stand to make money if you can sucker people into betting on them because of their unintuitive answers. A classic one is (when there are 23 or more people in a room): "I'm willing to bet you there are at least two people in this room with the same birthday. What odds will you give me?"
I've never been much for bar bets, but one summer I made up a puzzle to save myself some money. At camp, kids would come up to me and say "Do you have change for a quarter?" If I said yes, they would say, "Good, then you can lend me a quarter." And I would never see the quarter again. After awhile I started answering their question this way:
"Actually, I have the largest amount of change in my pocket for which I can't give you change of ANYTHING. How much change do I have?" And while they were pondering, I would sneak off. With quarters, dimes, nickels and pennies, you can have over a dollar and not be able to change a nickel, dime, quarter, fifty cent piece or dollar. What collection of change did I (pretend to) have?
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