Charles L. Bouton: 2 puzzles worth knowing

2 puzzles from Charles L. Bouton, each explained in a minute and credited to the original work. Free on Savvy.

A game where you can calculate who wins before either player makes a move
Two players take turns removing any number of objects, at least one, from a single pile they choose among several laid out at the start. Whoever takes the last object wins. With th…
— Charles L. Bouton, Nim, A Game with a Complete Mathematical Theory
Two players take turns removing objects from piles. One strategy always wins.
In Nim, players alternate removing any number of objects from a single pile, and whoever takes the last object wins. With several piles at once, is there a reliable way to know whe…
— Charles L. Bouton, Nim, A Game with a Complete Mathematical Theory

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