Posted by: sandeepchrao | December 9, 2008

My Reading Project

My project summarized the article, “The Group of Automorphisms of the game of 3-dimensional tick tack toe” by Silver.

Here is the link to the pdf.






  1. I love the rich language in this subject: rich and poor lines, evisceration and scrambling. The colourful metaphors help make it understandable too. So, as you can see from this article and many of the others students read, you can set out to figure out the automorphism group of almost anything you can imagine! Games and puzzles are especially common subjects. Often the method is to relate the group you are studying to S_n. But here the group is described in a hands-on way. The nice thing about this analysis is how the structure became clear once names were given to the right ideas (like rich points and full lines). Naming things is very important in mathematics.

    The outline of the proof is a nice trick, too: show that G = H (where you know H is a subgroup of G to start with) by showing that the inverse of every element of G lives in H.

    Reducing the number of distinct board positions through symmetry is incredibly important in analysing games. Sometimes for fun I’ve analysed certain board games with friends, and the first step is always the sort of thing this paper does: simplify the question using symmetry. That’s a mantra that applies in a much wider arena too.

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