##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Jason Lee

#### UCSD Graduate Student

## Combinatorial Game Theory: Arithmetic with Nimbers

##### Abstract:

A combinatorial game is a two-player game with perfect information and no chance elements. The players take turns making moves under clearly defined rules, and the last player able to make a move wins the game. NIM is one of the most well-known combinatorial games, and many people know that optimal play in Nim involves an addition operation which is just an XOR operation in disguise. Nim has a richer structure than this, however, as there is also a multiplication operation, and some unexpected and delightful things pop up such as Fermat powers (numbers of the form $2^{2^n}$). We'll explore nim fields -- finite fields of objects that aren't numbers, but NIMBERS, and really bizarre things happen -- even if I could convince you that 4 times 4 is 6, could you ever believe that the cube root of the nimber 2 is infinity? \vskip .1in \noindent Refreshments will be served!

Host: Audrey Terras

### November 24, 2004

### 11:00 AM

### AP&M 2402

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