Nim

Matchstick games

Nim — from the book's pages

• Any number of matches are laid out on the table in groups, not necessarily the same number in each. Each player in turn takes some of the matches, or all the matches, in one group. Whoever takes the last group or the last match wins — or loses, if the game is played the other way round.
• A variation lets a player split a group in two instead of taking. Before the game starts, the players must agree on how: only groups with an odd number, only into unequal parts, or freely.

Nimbi — from the book's pages

• Nim was solved by Charles Leonard Bouton in 1901; Piet Hein revived it as nimbi, which cannot be won with a formula. The matches are laid out in a rectangle. The two players in turn take any number of matches lying next to each other, from any row or column. If there is a gap in the row, the whole row cannot be taken at once. Whoever takes the last match has won.

Squayles — from the book's pages

• 31 matches in a rectangle of 12 squares. The players in turn take as many matches as they wish, provided they lie end to end and are taken in sequence. It is possible to take 21 in one go.

My choices

• Nim opens with the book's groups 4, 6, 5, 7 and 3. The machine works nim out completely, also with splitting and in the reversed game.
• Nimbi on 3 × 3, 4 × 3, 4 × 4 and 5 × 4 — the machine works the small boards out completely; on 5 × 4 it thinks for up to a second and a half and guesses the rest. Bouton is right about nim, Piet Hein about nimbi: the formula does not apply there.
• Squayles: a chain is matches lying end to end, one after another — tap them in the order you take them. The book does not say who wins; here whoever takes the last one wins. The machine looks two moves ahead and settles for chains of at most eight.

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