Question 43
In a tournament organised among 6 teams, each team plays against each other team exactly once. When a team wins, it gets 3 points, and the losing team receives 0 points. If the game is a draw, both teams receive one point. Determine the values of $a$ for which it is possible that the final scores of the teams are the six consecutive numbers $a, a+1, \ldots, a+5$.