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The match game

The match game

John and Smith are playing the match game of which John is an expert player. The game consists of removing 40 matches from the table by taking turns 1, 3 or 5 matches in each turn. The one who removes the last group of matches is the winner.

John, who does not like to lose, offers his friend an advantage and allows him to take the first turn in which Smith pulls 3 matches from the table.

Who will win the game?

Solution

Since John is an expert in this game, it is expected that he knows that as always an odd amount of matches is withdrawn, the only player who can win is the one who plays in second place since the target number is 40, an even number and with the Proposed game system, the first player will always leave an odd number of matches on the table while the second player will always leave an even number (or zero).