Fibonacci Nim: The Game

Discussion in 'Off Topic' started by it'ship2b^2, Feb 17, 2011.  |  Print Topic

  1. it'ship2b^2
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    it'ship2b^2 Silver Member

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    Here are the rules:

    1) Start with any number of sticks, chips, or pennies which is not a Fibonacci number. (a Fibonacci number follows the pattern: F(1)=0, F(2)=1, and F(n)=F(n-1)+F(n-2) so each term is the sum of the previous two numbers).
    2) The first person takes any number of sticks/chips/pennies away.
    3) The next person can take any number of sticks/chips/pennies between 1 and twice the number that the last player took.
    4) Repeat (3) until there are no sticks/chips/pennies remaining. The person to take the last stick is the winner.
    5) The winner picks the new number and the game begins again.

    Let's start with the number 50.

    I take 2 which leaves 48 sticks.
     
  2. SoFlyOn
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    SoFlyOn Silver Member

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    I take 3 which leaves 45 sticks.
     
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  3. it'ship2b^2
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    it'ship2b^2 Silver Member

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    I take 5 which leave 40.
     
  4. SoFlyOn
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    SoFlyOn Silver Member

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    I take 9 which leaves 31
     
  5. it'ship2b^2
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    it'ship2b^2 Silver Member

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    I take 4 which leaves 27.
     
  6. SoFlyOn
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    SoFlyOn Silver Member

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    I take 7 which leaves 20.
     

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