Help needed in understanding S-Grundy Number , any good tutorial.
I am trying to solve Mathalon Problem 146 S-Grundy Game (dead link).
I've included this in some other answers of mine, but figured it might be able to stand on its own as a community-wiki resource list.
Some resources describing the strategy for Nim and the Sprague-Grundy Theorem and how they can be applied to other impartial games can be found at one or more of the following:
If you learn about Nim and the Sprague-Grundy theorem and how they work together, then the next thing to learn is about octal games. Because of the strategy for Nim (how Grundy values combine), it suffices to know the Grundy/Nim values for a single "heap". If you calculate enough of these for many octal games, you often see a pattern. The sequence appears to be eventually periodic. There is a theorem attributed to Guy and Smith that says an apparent periodicity that goes on for long enough is guaranteed to continue forever. You can read about it on page 11 of Misère Games and Misère Quotients by Aaron N. Siegel, in this blog post of mine or as Theorem IV.2.7 in the graduate textbook "Combinatorial Game Theory" by Aaron N. Siegel.