The present essay is the expanded version of an answer to the question, which appeared on Quora, english edition: How does one realize that XOR is needed to solve the game of Nim? Nowadays, the interest on Nim does not seem to be very high, but my approach is that questions on Quora are just pretexts for me to study some problems I have heard about years ago, without ever having the time to look at them in depth. My story with Nim, for example, goes back to the Seventies. It stayed in the back of my mind for fifty years and now comes out. The present essay is an elementary introduction to Nim, but at least it leads you into the “machinery” of the game and, I hope, will leave no question totally unanswered.

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