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Codeforces
The Intuition Behind NIM and Grundy Numbers in Combinatorial Game Theory
There are already many wonderful resources online for learning the basics to combinatorial game theory, but the intention I have for this guide in particular is to try to make them more intuitive. Why does XOR work for Nim? Why does mex produce the Grundy numbers? When it was taught to me, it was more or less just as 'magic' to memorize, but now I think I have a decent understanding of why they are true, so now that I have a grasp of the intuition behind it, I decided I should record my thoughts into a blog.
There are already many wonderful resources online for learning the basics to combinatorial game theory, but the intention I have for this guide in particular is to try to make them more intuitive. Why does XOR work for Nim? Why does mex produce the Grundy numbers? When it was taught to me, it was more or less just as 'magic' to memorize, but now I think I have a decent understanding of why they are true, so now that I have a grasp of the intuition behind it, I decided I should record my thoughts into a blog.

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- Aug 17, 2024