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Thread: Urgent Pre-Caluculus problem help

  1. #1

    Urgent Pre-Caluculus problem help

    There is a game in which two people can play. One person writes down a positive integer. The second person looks at it and decides whetherto go first or second. The players then take turns subtractig powers of 2 (i.e. 1,2,4,8,16,... no fractional or negative powers allowd) from the original number. negatives are not allowed and the player who gets to 0 wins. Assuming both players are playing to win and you did not write down the numebr:

    1. What should you do if 3 is the chosen number?
    2. What should yo do if 5 is the chosen number?
    3. What are all the starting numbers from 1-20 in which you would want to go first?
    4. Develop a plan of whether to go first or second for all starting numbers from 1-100.
    5. If you played the game by subtracting powers of 3, what would your strategy be?

    I need to prepare a document to explaining the solution to all of the above problems. Please help....
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  2. #2
    Junior Member
    Feb 2006
    United Kingdom
    what have you tried doing so far? have you tried experimenting with playing the game with yourself? this is how you're supposed to work things out. for instance i shall start you off.

    if 3 is the chosen number... you can either pick 1 or 2..
    say i pick 1
    3-1 = 2.... my opponent can win next turn
    if i pick 2
    3-2 = 1... my opponent can win next turn
    he who goes first loses, so choose to go second.
    if 1 is the chosen number. go first since you can get out in one go.
    if 2 is the chosen number. go first since you can get out in one go.

    so try doing it for all the numbers from one to twenty, and trying all the possibilities, and seeing if it would be best to go first or second.
    then once you've done this see what you notice about your results. maybe you will see a pattern.
    good luck.
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