From [1] and [3]: The team that lost the greatest number of games lost the two games it played (there were three losers and the teams could not have each lost one game). So the team that lost the greatest number of games did not score 6 and did not score 5 and 4 together. The highest total of two scores achieved by this team is greater than the total of at least 7 (6 and at least 1) achieved by some other team. So this team scored 5 and 3 for a total of 8. Then the 5 score lost to the 6 score and the 3 score lost to the 4 score. So the 1 score and the 2 score go together and the 6 and the 1 were scored by the same team. Let the teams be X,Y, and Z temporarily; then in summary:

From inspection of the team score, any two higher scores differ by at least one and at most two; any two lower scores differ by at least one and at most two. So, from [2], the Angoras’ higher score and the Bobcats’ higher score differ by two and the Bobcats lower score and the Cougars lower score differ by one. So the Angora must be Z, the bobcats must be Y, and the Cougars must be X. Then the Cougars achieved the highest total of its two scores.