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I'm trying to work out the maximum number of unique combinations for the following rules. This is part of me learning python.

There are $16$ teams $[1,2,3....16]$, the teams only play each other once, $\dfrac{n(n-1)}{2}$ is the maximum number of possible unique games $(120)$, this is a common round robin format.

There are only $8$ courts with $8$ concurrent games played each round, over $15$ rounds.

A team may only play on each court once.

How many rounds does it take before I run out of unique combinations.

The code gives me almost $4$ rounds or $31$ games out of a possible $64$ games for $8$ courts and $8$ rounds.

I want to be able to maximise number of unique combinations given the limitations on the number of grounds to test how efficient the code is working.

This is a bit of an edit on the original question as a few things became clearer after I mapped out the problem, see attached image.

map of court and team allocations by round just using best fit by round

This is the draw which is fixed

Jd Johnson
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  • How can you have a $15$ week period if each team can only play on each ground once, so has a maximum of $8$ games? – Ross Millikan May 04 '19 at 03:30
  • Thanks for the question, I perhaps should have just said 15 rounds. Its a lawn bowls question that I tried to make more understandable by using football terms. I will fix. – Jd Johnson May 04 '19 at 03:37
  • But if you have $15$ rounds, each team will play something like two matches on each of seven grounds and one on the last. You say they can each play on each ground once. Are you looking for the longest start of a round robin tournament that satisfies these constraints? – Ross Millikan May 04 '19 at 03:41
  • Scheduling tournaments is complicated business. When you write, "I want to calculate", I take it you are asking for a simple formula. My guess is that no such formula is known that works for all possible inputs. – Gerry Myerson May 04 '19 at 03:46
  • Thanks Ross, yes that's a good way of putting it or how many rounds or games can I play before I exhaust all the unique combinations given the limitation of 8 grounds/courts. – Jd Johnson May 04 '19 at 03:49
  • Bumping the question three years later, did you find any solutions for this problem? – Stef May 03 '22 at 12:52

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