I'll give it a try (spoiler sketch, perhaps): If there is an optimal strategy S w/o communication and collusion, it should have the property that when two players play S, they are each guaranteed to win at least 1/3 of the time, while the third player can win AT MOST 1/3 of the time. We can assume the 3rd player, wlog, is playing a pure strategy. One strategy that satisfies the properties above is, "Pick number i with probability 1/2^i." On 1/12/07, Dave Dyer <ddyer@real-me.net> wrote:
The current puzzle at The Grey Labrynth is an amusing math puzzle.
http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=206
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