4 by 4 Combination Solvable or Unsolvable? I believe this problem is unsolvable (as in there is no correct solution).  Can somebody confirm that there is no solution?
If there were 4 Teams of 4 Players as follows...
Team A
Art (A1)
Andy (A2)
Angela (A3)
Adam (A4)
Team B
Brian (B1)
Brenda (B2)
Brady (B3)
Bobby (B4)
Team C
Carl (C1)
Connie (C2)
Colt (C3)
Cam (C4)
Team D
Dan (D1)
Dave (D2)
Debbie (D3)
Dennis (D4)
If they each play in a 4-Player game is there any combination of game pairings such that each player plays each player not on his team exactly once?
-Brian
 A: Here is a solution:
First round    Second round   Third round   Fourth round
-----------    ------------   -----------   ------------
A0,B0,C0,D0    A0,B1,C2,D3    A0,B2,C3,D1   A0,B3,C1,D2
A1,B1,C1,D1    A1,B0,C3,D2    A1,B3,C2,D0   A1,B2,C0,D3
A2,B2,C2,D2    A2,B3,C0,D1    A2,B0,C1,D3   A2,B1,C3,D0
A3,B3,C3,D3    A3,B2,C1,D0    A3,B1,C0,D2   A3,B0,C2,D1

Each round looks like:
A0,Bx,Cy,Dz
A1,B-,C-,D-
A2,B-,C-,D-
A3,B-,C-,D-

and the indices of the players in the lower right 9 positions (indicated by - in the general shape) is always the binary XOR of the A player in the game and the index of the player from their own team who meets A0 in that round.
(This use of XOR is why I renumbered the players from 1-4 to 0-3).
I believe this is the unique solution, up to permutations of the rounds and permutations within each team. In particular, by exhaustive search I think for any solution it's always possible to renumber the just the players such that the first two rounds are exactly as above; the third and fourth then seem to be forced to be the above ones too.
