

Sprague-Grundy theory (on the equivalence of certain games) - eru
http://blog.plover.com/math/sprague-grundy.html

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ig1
I previously considered doing a phd is a closely related area, I think there's
a huge amount of potential when it comes to looking at the underlying
structure of games and their equivalences.

Imagine you had two games which had the same underlying graph of positions,
but two very different representations (so say a subset of a game like Chess
and a subset of a game like Hex). You'd know that the two games are equivalent
and there's a one-to-one mapping, they should have exactly the same
difficulty, but some humans would find one easier than the other.

This would give us a great insight into how people think, and help us
understand the relationship between the representation of a problem and it's
underlying complexity.

~~~
eru
Like Northcott's game and bogus Nim?

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eru
So --- now take this theorem and find a solution to
[http://projecteuler.net/index.php?section=problems&id=26...](http://projecteuler.net/index.php?section=problems&id=260)

"A game is played with three piles of stones and two players. At her turn, a
player removes one or more stones from the piles. However, if she takes stones
from more than one pile, she must remove the same number of stones from each
of the selected piles."

(Please do not post complete solutions, as this is against the spirit of
Project Euler.)

