Homework Soursefor what values of mn can player 1 force a win in Nim mn And
for what values of m,n can player 1 force a win in Nim (m,n). And vice Versa for player 2.
for what values of m,n can player 1 force a win in Nim (m,n). And vice Versa for player 2.
for what values of m,n can player 1 force a win in Nim (m,n). And vice Versa for player 2.
Solution
Lemma 1.1 The nim position m,n is winning if and only if m 6= n, otherwise losing, for all m,n 0. This lemma applies also when m = 0 or n = 0, and thus includes the cases that one or both heap sizes are zero (meaning only one heap or no heap at all).
http://www.maths.lse.ac.uk/personal/stengel/lectnotes1-7.pdf
