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Oddwins (Posted on 2006-10-03) Difficulty: 3 of 5
A game of 11 marbles wherein each player can either pick one or two marbles from the total. Starting from Player A & then Player B alternatively. This continues till all the marbles are picked. The winner is the one having odd number of marbles.

What is the strategy to be followed for Player A & B to win?. What happens for higher total number of marbles (13, 15 etc )?

No Solution Yet Submitted by Salil    
Rating: 4.0000 (1 votes)

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Solution Almost mystic solution | Comment 6 of 11 |
How to win: if you have an even number of marbles, and there are 4K+1 marbles, pick 1 or 2; if there are 4K+2 marbles, pick 1; and in other cases pick whatever you will, but you'll lose.

If you have an odd number of marbles, and there are 4K marbles on the table, pick 1; if there are 4K+2 or 4K+3 marbles, pick 2; and if there are 4K+1... sorry, you'll lose.

I came to this strategy after much (essentially simple, but long and tedious) work with a states machine. [If there is interest I may try to write it up for a later message.]

If I am right, the first player wins for 13, 17, 21... and so on marbles, and the second wins for 15, 19, 23...

  Posted by Federico Kereki on 2006-10-03 20:24:41
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