“MY numbers!” (On the ownership of knowledge)

The other day, I presented some students with the following game:

Last cookie is a game for two players. In this game, a number of cookies are divided between two cookie jars, and each jar has at least one cookie. Each player can take cookie in one of two ways:

  1. By taking any number they like from just one jar or
  2. By taking the same amount from both jar.

The winner is the person who takes the last cookie(s).

Some of you may recognize this as Wythoff’s game; on the NRICH website, which has a great online version of the game, it’s called Last Biscuit (I modified the name for a Canadian audience). If you aren’t familiar with the problem, I highly encourage you to give it a go – very easy to understand and play, but the optimal strategy is not particularly obvious.

I assigned this game as homeplay (get it?? because it’s a game… terrible, I know). Then, the other day, we picked it up again after about a week of rumination.

https://i0.wp.com/alexmakarski.com/wp-content/uploads/last-cookie.jpg

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