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The nim-value, or Grundy number, is not the number of prime factors.
Take 8 for example.
8 = 2 * 2 * 2
As shown, 8 has only 1 prime factor, which is 2.
If we compute the Grundy number of a number n (G_n), we get
G_1 = 0
G_2 = mex({G_1}) = mex({0}) = 1
G_4 = mex({G_1, G_2}) = mex({0, 1}) = 2
G_8 = mex({G_1, G_2, G_4}) = mex({0, 1, 2}) = 3 != 1
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Tower Breakers, Revisited!
You are viewing a single comment's thread. Return to all comments →
The nim-value, or Grundy number, is not the number of prime factors.
Take 8 for example.
8 = 2 * 2 * 2
As shown, 8 has only 1 prime factor, which is 2.
If we compute the Grundy number of a number n (G_n), we get
G_1 = 0
G_2 = mex({G_1}) = mex({0}) = 1
G_4 = mex({G_1, G_2}) = mex({0, 1}) = 2
G_8 = mex({G_1, G_2, G_4}) = mex({0, 1, 2}) = 3 != 1