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playing for sticks


I lay out twenty sticks on the table and we play a "pick up the sticks game." You can pick 1, 2, 3, or 4 sticks during your turn, and the loser is the person who is left with the last stick laying on the table. If I let you pick up sticks first, how can you devise a strategy to win every time?

 

 Extensions

Suppose you can choose the number of sticks at the start of the game. If your opponent goes first, then how many sticks do you want to use at the start of the game in order for you to win every time?

How would the strategy change if you could pick only 1,2, or 3 sticks during your turn?



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