Back when I was still in middle school, I was sitting at my kitchen table during a family gathering, and my uncle posed the following puzzle for me to solve: A vendor is selling apples for 10 cents apiece, oranges for 5 cents apiece, and peanuts two for a penny. Someone comes along and buys exactly 100 items for exactly one dollar. How many apples, oranges and peanuts did that person buy? I took out a sheet of paper and a pencil and came up with the answer in a couple of minutes. This astonished my uncle because, it turns out, he had posed this problem to two adults, including a geometry teacher, and they couldn't solve it in less than a half hour. I had a bit of a reputation for mathematical cleverness, and he had posed this problem to stump me and test the extent of my cleverness. Decades later I still remember exactly how I solved it, probably because it was a boost to my ego to learn that I was apparently smarter than a geometry teacher! In this article... read more