Many many years ago when I was in elementary school, my teacher decided to test the class by sending us home with a math problem that was far above our heads. It was a just-for-fun challenge that we knew we probably wouldn't be able to solve. In retrospect, I think it was just a ruse to occupy us with busywork at home that night. It worked.
I stared at that stupid problem for hours but I didn't make much progress. It required algebra, see, and I had never heard of such a thing. I did make some progress inventing an extremely primitive sort of algebra on my own, but it wasn't getting me very far. Finally I showed the problem to my father and he sat down to work. He wrote out some equations, did some sort of voodoo, and before I knew it he had an answer. It took him a while to convince me that it was the correct answer, but eventually I understood that all those numbers, letters, and symbols proved his point.
I want to share the problem with you. Can you figure it out? Here it is:
A rope over the top of a fence has the same length on each side, and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkey's mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey, plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkey's mother is one-half as old as the monkey will be when it is three times as old as its mother was when she was one-half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one-third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one-fourth as old as it is now. How long is the banana?