document.write( "Question 457405: My question is I'm playing a game, 1-100, there's two people, we can choose an integer between 1 & 9, how do I make sure I win?
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Algebra.Com's Answer #313864 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
This game is rigged from the very start.
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\n" ); document.write( "The trick is to be the first person to add a number such that the total at that point in time is some multiple of 10. That is to say, after you add your number the total is 10 or 20 or 30 or 40 or 50 or 60 or 70 or 80 or 90. From that point on the game is effectively over.
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\n" ); document.write( "I'm not sure whether the rules say that the game starts at zero or 1. If it starts at zero, let your opponent go first. Whatever number your opponent selects, you choose your number such that the sum of the two numbers (your opponent's and yours) is 10. From that point on, when your opponent chooses his or her next number, you select your number such that when it is added to your opponent's last selection, the total is 10. Eventually you will get to the point where your number when added to the total results in the new total of 90. Your opponent can then add any number from 1 to 9 but he or she will not be able to reach 100. Then you will be able to add the last number to make the total 100.
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\n" ); document.write( "If the game starts at 1, you need to go first if you are to ensure a win. Add 9 to the starting point (making the first total reach 10) and you have won the game by just using the strategy that whatever number your opponent chooses, you follow it with the number that when added to your opponent's last choice adds up to 10.
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\n" ); document.write( "In any case, you need to hope that you are the first one to add a number such that the total is some multiple of 10. When you do that, you have taken control and will win the game by selecting your numbers such that when added to your opponent's last selection sum to 10. If your opponent chooses 1, you choose 9. If your opponent chooses 4 you choose 6. If your opponent chooses 8, you choose 2, and so forth.
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\n" ); document.write( "Think about this strategy a little bit and it will become clear to you what is going on.
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\n" ); document.write( "Hope this helps you to understand the fundamental strategy for winning, but the strategy is simple enough that your opponent will probably figure it out pretty fast if he or she doesn't know it at first.
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