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?
