Nim

Matchstick games

Nim

• The matches lie on the table in groups. The groups do not have to be the same size.
• On your turn, choose one group and take as many matches from it as you like: one, a few, or the whole group.
• Whoever takes the last match wins. You can also play the reversed game, where whoever takes the last match loses.
• If the players agree, a turn may split a group into two smaller groups instead of taking from it. Decide before the game how: only into unequal parts, only groups with an odd number of matches, or freely.

Nimbi

• The matches lie in a rectangle of rows and columns.
• On your turn, take any number of matches lying side by side in one row or one column. They must be neighbours: where a match is already gone, the gap cannot be taken across.
• Whoever takes the last match wins.

Squayles

• 31 matches form the sides of a grid of 12 squares, four across and three down.
• On your turn, take a chain: one match, or several lying end to end, each one starting where the one before it ends. A chain may turn corners, and it may be long — more than twenty matches can go in a single turn.
• Whoever takes the last match wins.

In this version

• Nim starts with five groups of 4, 6, 5, 7 and 3 matches. Charles Leonard Bouton solved nim in 1901, and the machine plays it perfectly, with splitting and in the reversed game too.
• Piet Hein made nimbi so that no formula would win it. You can play on 3 × 3, 4 × 3, 4 × 4 or 5 × 4. The machine works the smaller boards out completely; on 5 × 4 it thinks for up to a second and a half and guesses the rest.
• In squayles, tap the matches in the order you take them. The machine looks two moves ahead and keeps its own chains to eight matches or fewer.

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