This is a good point. When I was a schoolboy, there were three of us who used to rotate fairly regularly at the top of the chess ladder. This was because our styles and knowledge (e.g., of openings, endgames, etc.) were such that almost invariably B beat C, C beat A and A beat B. R. On Fri, 27 Aug 2004, Paul R. Pudaite wrote:
This assumes deterministic transitivity among the players, which is fine for a math problem, but may not be the best model for a tennis coach.
Paul
At 10:44 AM -0500 8/27/04, David Gale wrote:
Given n candidates trying out for a tennis team of t players. Find the minimum number of matches needed to pick out the top t.
I don't expect anyone to solve this. The related problem of picking the t'th best player remains unsolved for n >7. (see Knuth, vol. 3)What I noticed is,
1). The top t problem is strictly "easier" than the t'th best problem. Example. You can find the top 2 out of 5 in only 5 matches, (try it), whereas finding the second best requires 6 matches. 2).There doesn't seem to be any treatment of the top t problem in the literature. Knuth doesn't even mention it.
References, anyone?
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