## Two nice facts about games.

Since giving my talk last week about games, I’ve been on a bit of a mathematical gaming kick, and would like to share some of the gems I’ve come across. We’ll give a beautiful argument due to Gale about his game Chomp, and an exceedingly clever argument due to Hochberg, McDiarmid, and Saks which applies Sperner’s lemma to the Game of Y.

## Mathematics and Games (Kangaroo Math 2014)

On Sunday, March 23rd, 2014, I gave a talk to parents of kids writing the 2014 Kangaroo Math contest. The slides are available here: Kangaroo 2014 Slides. The content of the talk was a discussion of Tic-Tac-Toe in disguise, and a proof of the winning strategy for Nim.

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## Questions about Discs

Over the past couple weeks I’ve been asked a lot of questions about discs in Euclidean space. In this post we’ll be putting pennies on a table, refining covers of discs, and trying to cram lots of balls into high dimensional balls. Some open questions about putting pennies on tables occur below.

## The Pigeon Hole Principle

Below the cut are some pigeon hole related questions I collected together for a Math Circle at the Fields Institute.

## TwixT and Hex

Derek and I like to play abstract strategy games together. In highschool we both got hooked on Hex, a very elegant game with simple rules. Derek went so far as to beat Hexy on every single difficulty setting and board size — which is remarkable since Hexy plays well. Hexy has a really interesting approach to playing Hex that combines Shannon’s electrical resistance methods with automatic theorem proving techniques; you can read about it on the website. We usually play games on Richard’s Play by E-mail Server. So far we’ve played: Hex, Abalone, Y, Zèrtz, and TwixT. We both really like connection games ; Abalone and Zèrtz are the only non-connection oriented games on the list. We also used to try out games on PlayOK, back when it was called Kurnik and one could play Hex. We played a little Awari there, a beautiful african game I could never get the hang of.

A couple days ago, Derek started up play by e-mail boards that I haven’t got around to moving on yet. One 11×11 Hex board and a TwixT board. We’ve only played two games of Twixt thus far and I’m not sure that it suits my tastes. This third round might be the one that decides how I feel about the game. Right now I find the adjacency structure put on the grid by TwixT aesthetically unappealing. There are too many acute and obtuse angles for my liking.

Once we’ve played out the two matches, hopefully I’ll post a commentary.

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