Hey, I'm interested in Math problems, and I solved thisproblemin "536 puzzles & curious problems":

Seven men engaged in play. Whenever a player won a game he doubled the money of each of the other players. That is, he gave each player just as much money as each had in his pocket. They played seven games and, strange to say, each won a game in turn in the order of their names, which began with the letters A, B, C, D, E, F, and G. When they had finished it was found that each man had exactly $1.28 in his pocket. How much had each man in his pocket before play?

Here's The solution:

I've worked this solution using a table, and noticed the strange behavior.As you can see,1.28$ = 128 cents = 2^7, and there are 7 players, playing 7 games. To make sure this isn't a coincidence, I worked a scenario where 8 players play 8 games, and each end with 2^8 = 256 cents. Sure enough, the last player started with 8*1 +1 = 9 cents, the next 8*2 +1 = 17 cents, the third 8*4 +1 = 33 cents.

I've been fiddling with this for the last two days, and I still can't see why it behaves this way?!

This isn't homework, mere enthusiasm. If you could explain this mystery for me, I would be most grateful.