Dear Funsters, Progress on an outstanding Mixed doubles scheduling problem was made at the recent Gathering for Gardner (G4G9). The problem is to schedule 20 mixed doubles participants in as many rounds as possible, with all players participating in each round but never playing with the same partner or facing the same opponent twice. A player is permitted to play with and against the same player in different rounds. An upper bound is 9 rounds as there are only 9 same sex opponents available. As reported in A lifetime of Puzzles (Demaine, Demaine, Rodgers) (2008), the best solution known was 7 rounds. At G4G9 I had the luck to sit next to Josh Purinton (josh@purinton.org) and gave him the problem. In less than 24 hours he had sent it to a solving algorithm and produced the table below. This still leaves open the question if the maximum of 9 rounds is possible. Also an open problem is whether 9 rounds is possible for men's or women's doubles. I invite funsters to cogitate and comment. Happy puzzling, Dick Hess Best Known Mixed Doubles Scheduling for 20 Players Court 1 Court 2 Court 3 Court 4 Court 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 10 17 18 3 12 19 4 5 8 13 2 9 16 17 6 11 20 15 19 1 16 19 2 3 6 17 10 5 18 15 12 7 20 11 8 9 14 13 4 1 4 15 6 3 14 5 12 7 16 9 20 11 10 17 2 13 8 19 18 1 20 5 10 3 8 11 16 7 12 15 2 9 6 19 14 13 18 17 4 1 14 17 8 3 2 15 18 5 20 9 4 7 10 19 16 11 6 13 12 1 12 13 20 8 18 7 14 5 4 17 16 9 8 15 10 11 2 19 6 1 8 9 12 3 20 13 6 5 16 4 18 7 2 17 14 15 4 19 10