In case anyone is interested, here is how I solved the problem. I will present the solution for a 3 round tournament. The generalization should be fairly obvious. Suppose there are only 2 players. Then there is only one game, [1,2]. For four players, think of [1,2] as a possible second round matchup. In the first round, 1 and 2 play 3 and 4. There are two ways of doing this. I am just going to add 2 to 1 and 2 to get: [1,3][2,4] For 8 players, think of [1,3][2,4] as a possible second round outcome. In the first round, players 1 to 4 play against 5 to 8. Maintaining the order of the four team result, just add 4 to get [1,5][3,7][2,6][4,8]