High school proof for Sprague–Grundy theorem

Asked Jul 23 '17 at 16:40

Active Jul 23 '17 at 16:40

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I'm having a hard time trying to understand the proof given in Wikipedia, I have never seen that notation before. I'm having the same problem with other sources.

I completely understand the proof of winning and losing states of Nim game (using XOR) but I can't understand the proof that "every impartial game under the normal play convention is equivalent to a nimber" 1. I wonder if there's any high school proof for that.

asked Jul 23 '17 at 16:40

M. M

1

This doesn't give a proof but it does give an explanation that might make the proof easier to read. – MJD Jul 23 '17 at 16:48
Thanks @MJD, I'll take a look. – M. M Jul 23 '17 at 16:57
A number of different sources are available at this community wiki post. If any of them work for you, or if you find another source that does, I recommend posting an answer to your own question. – Mark S. Sep 15 '18 at 18:30

High school proof for Sprague–Grundy theorem

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