combinatorics - Weekly group assignment algorithm with odd number of participants -
there round-robin solution question i asked before . works great number of people none of suggestions seem work once implement algorithm , try them out. i've tried many variations , (grouping last 1 whole bunch of other people, second group last group, different combinations, 2 , 4 last of bottom row, thought give me optimal solution still many duplicates). can suggest way go, or proof there cannot solution without 2 people working more once can stop trying make work. if want algorithm in java can post can play it. thanks. 14 weeks 23 students in groups of 2 , 1 3 sufficiently undemanding local search able find solution. 18 1 11| 3 4| 5 7| 9 6| 0 17| 2 12| 10 19| 15 16| 21 8| 14 20| 13 22| 6 13 18| 17 4| 5 0| 20 1| 12 11| 10 9| 2 14| 15 7| 3 8| 19 16| 21 22| 21 17 7| 19 22| 3 1| 2 8| 0 10| 14 12| 13 11| 6 16| 5 15| 18 20| 9 4| 8 1 13| 18 2| 6 11| 20 0| 12 10| 14 15| 5 17| 9 21| 4 19| 3 22| 16 7| 0 4 16| 17 20| 21 3| ...