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A107431
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Triangle read by rows: T(n,k) = maximal number of rounds for the social golfer problem with n groups of k golfers (n >= 2, 2 <= k <= n).
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3
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3, 5, 4, 7, 4, 5, 9, 7, 5, 6, 11, 8, 7, 6, 3, 13, 10, 9
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OFFSET
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2,1
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COMMENTS
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The problem is to find the largest number of rounds of golf that can be arranged with n*k golfers who play in n groups of k. No golfer may play in the same group as any other golfer twice (i.e., maximum socialisation is achieved).
T(6,6) cannot be 4 since this would be equivalent to a pair of mutually orthogonal Latin squares of order 6.
T(n,k) = 1 for values of n and k outside this range.
The next term T(7,5) is known to be either 7 or 8.
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LINKS
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EXAMPLE
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Triangle begins:
3;
5, 4;
7, 4, 5;
9, 7, 5, 6;
11, 8, 7, 6, 3;
...
T(2,2) = 3 from { 12/34, 13/24, 14/23 }.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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