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The daisies game

The daisies game

Sometimes they ask me how I can think of the subject of riddles. For example, I have a few Swiss-themed riddles that go on flags, cheeses or alpine roses. Well, believe me if I tell you everything, it's because of a little anecdote that happened to me more than a quarter of a century ago.

I went with a group of Swiss with whom I was touring the Alps and we took the dangerous route from Altdorf to Fluellen, to visit the historic place where William Tell shot at the apples. When we stopped to rest I saw a girl who was picking daisies. To entertain her, I taught her to predict her future marriage by plucking the petals of a daisy to know if she would marry "a rich man, a poor man, a beggar or a thief." He told me that he already knew how to play that game, that all the girls in the place knew him, with the difference that there the players could start one or two contiguous petals, until the winner tore the last and leave the stalk, or "spinster", to his opponent.

I could not win our little math, who was not more than 10 years old, not once. And it wasn't until I reached Luzerne that I started thinking about the trick.

I show you the game in the drawing, in which you have a 13 petal daisy. It is played by two people, who will remove one or two adjacent petals until there is none left to remove. Whoever stays with the last petal wins and leaves the spinster stalk to his opponent.

The one who starts playing can decide whether to start by pulling one or two petals. So the riddle is to say what system do we have to follow to win even if we don't start

Solution

The secret is to divide the petals into two equal groups. For example, if the first player starts the petal number 1, the second must start the petals 7 and 8, but if the first player starts the petals 1 and 2, the second will start the 8. Thus we will always have the flower divided into two groups 5 petals

From there, just imitate the first player's moves. If the first player starts two petals to leave a 2-1 combination in one group, the second starts the two corresponding petals to leave a 2-1 combination in the other group. So the last play will always be yours.