3 Jan
2007
3 Jan
'07
12:15 p.m.
Since RKG didn't say it, let me give the three-line explanation of why the option to split piles doesn't matter: In regular nim, you may change a pile of size n to one of size m for any m<n. Here you may also split it into piles of size m1, m2 with m1+m2 < n (regular addition), but these two piles are equivalent (by induction) to one pile of size m1 (+) m2 (nim-addition), which is also <n. Every move in the new game is therefore equivalent to one that was already available; you can win by simply playing nim and ignore the fact that the other player may occasionally make a move you hadn't known existed. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.