Penny Pinching

The game of Penny Pinching goes like this: I put out a pile of pennies, any number of pennies I like. Then you, after seeing how many I put out, put out another pile of pennies, as many as you like. Then I make the first move. A move consists of removing any number of pennies I choose from either pile, or the same number of pennies from both piles, but at least one penny must be taken per move. After I move then you move, and we alernate turns until all the pennies are gone. The winner of the game is the player who takes the last penny.

Given these rules, if you fully understand this game, you can beat me every time. The problem is to find out just how to do that. You will need to develop a strategy that tells you what move to make in any possible situation. To keep things reasonable, it’s ok to limit the problem to no more than 100 pennies total.

Lennart J. has solved this game! Here is his spreadsheet that you can play:  PennyOpponent.xls

This spreadsheet uses macros, so you may have to adjust your security settings to allow it to run.

Go to: Tools Menu / Options / Security Tab / Macro Security Button / Set to: Medium