How to always win at the game of matches

How to always win at the game of matches

The rules of the game of matches are very simple: a certain number of matches are spread out in a row and each of the two players must take turns choosing between removing one, two or three. The player who removes the last match, loses. (Of course, the game can also be played with chopsticks or any other object.)

It seems that the winner of the game will be the result of chance, however, applying mathematics you can become the unbeatable winner .

Mathematics and matches

Until we collect five matches, games with fewer matches will always give the same result: the first player to move wins. But after five, then you have to look for strategies. The first player has to remove 1, 2 or 3 matches, which means that he leaves the opponent 4, 3 or 2.

In those three situations, however, the player who has to move can ensure victory. The position is therefore a loser for the first player, exactly the same as in the case of only one match remaining: unless the contrary is wrong, the person who plays first loses .

If the game started with 6, 7 or 8 matches, the first player can again ensure victory, leaving 5 matches to his opponent.

Fire 684 014 960 720

With 9 matches, the first player loses, because he has to leave 6, 7 or 8 matches to the contrary. It is therefore won by playing second.

If you start with 10, 11 or 12 matches, it is the first player who can be sure of winning, just by leaving 9 matches; with 13 the winner is second, and so on. As Robin Jamet concludes in his book Hidden Mathematics :

In short, if the starting number of matches is any of the series 1, 5, 9, 13, 17 … (that is, the numbers that can be written as a multiple of 4 plus 1), the position is losing for the first player; in the other cases it is the winner.