The Last Match

In this game, can you figure out how to make sure that your opponent always picks the last match?

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Arrange fifteen matches side by side on a table. Tell one of your friends that you can always make him pick up the last match, each of you alternating in picking up one, two or three matches at a time. It doesn't matter who starts.

Materials: Fifteen matches.

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The secret of this trick is to make certain to leave five matches on the table for your opponent the third time around. Then, no matter how many matches he picks up, he will lose the game. For instance, if he picks up one, you take three, leaving the last one for him. Or if he picks up two, you take two. If he picks up three, you take one. In each case, the last match is left for him.

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Following are two of the several combinations you can use to arrive at the point of leaving the five matches for your opponent.

            Opponent                     You                              15M
            (3                                 1                                  (11
            Take (2                        2 Leaving                     ( 7
            (1                                 1                                  ( 5
                                               
                                                Or

            (1                                 2                                  (12
            Take (2                        1 Leaving                     ( 9
            (3                                 1                                  ( 5

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