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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