On Monday, September 15, 2003, at 03:52 pm, Richard Guy wrote:
If you want more symmetry, put them at the vertices of a regular 2n-gon and pair i with 2n-1-i, giving n parallel chords, which rotate much as before. For an odd number, 0 doesn't get to play -- his opponent having the bye.
For 2n people, this always pairs players of opposite parody (no matter how you rotate it). So the rotations of this only get you to play half of the people in the group. The simple fix is to also take the pairings of i with 2n-i, except that this leaves out 0 and n. Well, it pairs them each with themselves. You could give both of them byes, and get a nice symmetric tournament -- but one that that takes a full 2n rounds, instead of the 2n-1 that you get if everyone plays every time. --Michael Kleber kleber@brandeis.edu