💡📝Greg Strong wrote on Sat, Jun 24, 2017 03:15 AM UTC:
Sorry, guys, but I've hit another snag.
The odd number of players doesn't work, so I was going to drop SxG, on the basis that he was the latest joiner, so he should be the one to be dropped.
Then I turned to generating the pairings. Been struggling with it for hours, with no success. Eventually I discovered that the problem was not solvable. The parameters: 10 players, 9 games, no players play each other more than once. Seems like this is possible, but it's not. Number of games = 3 rounds of 3 games with 5 pairings in each = 45 total games. What are the number of unique pairings? 9+8+7+6+5+4+3+2+1 = 45! Ok, so 45 games and 45 unique pairings - great, right? No, because there is the additional restriction that the pairings are grouped into the 9 games. Not possible.
This problem is surmountable if we allow pairs of players to play more than one game. But it's late, and I'm pretty intoxicated, and the mathematics elude me at the moment. So I'll attack this tomorrow. Maybe, if we're really lucky, Daniel will turn back up by then and confirm his participation, and the whole problem will go away, as with 12 players, the number of pairings will far exceed the number of games.
Incidentally, if anyone knows how to contact Daniel MacDuff, that would be awesome.
Sorry, guys, but I've hit another snag.
The odd number of players doesn't work, so I was going to drop SxG, on the basis that he was the latest joiner, so he should be the one to be dropped.
Then I turned to generating the pairings. Been struggling with it for hours, with no success. Eventually I discovered that the problem was not solvable. The parameters: 10 players, 9 games, no players play each other more than once. Seems like this is possible, but it's not. Number of games = 3 rounds of 3 games with 5 pairings in each = 45 total games. What are the number of unique pairings? 9+8+7+6+5+4+3+2+1 = 45! Ok, so 45 games and 45 unique pairings - great, right? No, because there is the additional restriction that the pairings are grouped into the 9 games. Not possible.
This problem is surmountable if we allow pairs of players to play more than one game. But it's late, and I'm pretty intoxicated, and the mathematics elude me at the moment. So I'll attack this tomorrow. Maybe, if we're really lucky, Daniel will turn back up by then and confirm his participation, and the whole problem will go away, as with 12 players, the number of pairings will far exceed the number of games.
Incidentally, if anyone knows how to contact Daniel MacDuff, that would be awesome.