Question 575099: The following is a two-player game. Player One chooses a whole number from 1 to 8. Player Two adds from 1 to 8 to that number. The players then alternate adding from 1 to 8 to the current total. The object of the game is to make the total exactly 64 on your turn. If you are Player One, what number should you choose at the beginning of the game in order to guarantee a win for yourself? I tried them all and Kat always wins.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You start by choosing 1.
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From then on, whatever the second player chooses, your next number should be such that when you add it to the second player's choice, the total is 9.
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For example, you start by choosing 1. Then the second player chooses 2. You then choose 7 because 2 + 7 equals 9. Next the second player chooses 5. You then choose 4 because 5 + 4 equals 9. Then second player chooses 8. You then choose 1 because 8 + 1 equals 9. And so on.
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Think about this. You began with 1. After that every two choices (his and then yours) adds 9 more. So the game will score as follows:
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1 + 9 + 9 + 9 + 9 + 9 + 9 = 55
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This means that after you make the last selection in this series, the total will be 55. After that, whatever number your opponent chooses (1 through 8) will make the total be from 56 to 63 and then it is your turn and you pick the appropriate number to make the total equal 64. You always win.
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Hope this helps you out.
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