A group of 2p people get together to play a chess tournament. In the first round, each person is saddled with exactly one game, so that p games are played. In how many different ways may this be done? Can you give a rigourous proof of your answer?

No clue on the problem. A feeling that it would be a series that somehow iterates on 3 because of that being the number of valid types of endings to a chess game? Just wanted to congratulate you on your star. Like the fractal too.

Originally posted by StarValleyWy No clue on the problem. A feeling that it would be a series that somehow iterates on 3 because of that being the number of valid types of endings to a chess game? Just wanted to congratulate you on your star. Like the fractal too.

The problem can be solved combinatorially if I had phrased it properly. When I say 'how many first rounds' I mean how many pairings are possible fro 2n players. Thank you for you congratulating me. I like the fractal too; you have good taste in computer-generated approximations to mathematical models of chaotic phenomena resulting from simple algebra ðŸ˜‰. Now if I can find a picture of myself that is not ASCII-ugly, I will put it in my profile ðŸ˜‰.

Originally posted by royalchicken The problem can be solved combinatorially if I had phrased it properly. When I say 'how many first rounds' I mean how many pairings are possible fro 2n players. Thank you for you congratulating me. I like the fractal too; you have good taste in computer-generated approximations to mathematical models of chaotic phenomena resulting from simple algeb ...[text shortened]... . Now if I can find a picture of myself that is not ASCII-ugly, I will put it in my profile ðŸ˜‰.

You can't mean how many possible first-round pairings are there from a pool with 2n contestants. Are you asking for a function that maps from the number of contestants to the number of unique final tournament tables (i.e., tables showing the progression from the first round of the tournament to its conclusion)?

Originally posted by bbarr You can't mean how many possible first-round pairings are there from a pool with 2n contestants. Are you asking for a function that maps from the number of contestants to the number of unique final tournament tables (i.e., tables showing the progression from the first round of the tournament to its conclusion)?

Originally posted by bbarr You can't mean how many possible first-round pairings are there from a pool with 2n contestants. Are you asking for a function that maps from the number of contestants to the number of unique final tournament tables (i.e., tables showing the ...[text shortened]... ression from the first round of the tournament to its conclusion)?

No; I'm asking for how many different sets of first-round games there can be, given that p games must be played, each player plays exactly once, and each player can either be black or white.

Originally posted by royalchicken No; I'm asking for how many different sets of first-round games there can be, given that n games must be played, each player plays exactly once, and each player can either be black or white.

the total number of possible pairings is 2(2p-1)-i think...hey-i'm bored and i can't be bothered thinking much justnow...ðŸ˜•