A Curious Mind W(o/a)nders

Friday, January 12, 2007

Games traders play!

Let's lighten the mood on this blog a little! Let's play a game :-)

1. There are 44 chips.
2. The first player may remove as many chips as desired, at least one chip, but the not the whole pile.
3. Thereafter, the players alternate removing, each player not being allowed to remove more chips than his opponent took on the previous move.
4. The player that removes the last chip(s) wins.

Hint: This is a simple example of a class of Impartial Combinatorial Games called “Dynamic Subtraction Games”…so you can crack it to win every time!

Happy playing :-)


  • At 2:34 am, April 02, 2007, Blogger Jochen said…

    What about: Take 4
    If he takes 4, take 4
    If he takes 3, take 1
    If he takes 2, take 2
    If he takes 1, take 1

    In every case, the remaining chips after your turn divided by the chips you took is even - so you win!
    If opponent switches to lower level, the chips after his turn divided by the amount of chips he took is uneven.
    E.g. first you take 4, 40/4= 10:even
    Then he takes 2:38/2=19:you win!
    If the remaining chips after his turn are not even (e.g. he takes 3 or 1), you take one and no-one is allowed to take more. So you win (uneven number!)

    If this is right, is there a mathematical proof??


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