When reading the interview with Vladimir Arnold in the April 1997 edition of the Notices, I came across the following anecdote.
Many Russian families have the tradition of giving hundreds of such problems to their children, and mine was no exception. The first real mathematical experience I had was when our schoolteacher I. V. Morozkin gave us the following problem: Two old women started at sunrise and each walked at a constant velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was the sunrise on this day?
I spent a whole day thinking on this oldie, and the solution (based on what is now called scaling arguments, dimensional analysis, or toric variety theory, depending on your taste) came as a revelation.
I found the solution in a rather straightfoward fashion, but I was curious as to the parenthetic remark. So, can anybody tell me (as a total outsider to algebraic geometry), what does this problem have to do with toric varieties?