In a tournament among six teams, every team plays against each other team exactly once. When a team wins, it receives 3 points and the losing team receives 0 points. If the game is a draw, the two teams receive 1 point each.
Can the final scores of the six teams be six consecutive numbers a,a+1,...,a+5?
If so, determine all values of a for which this is possible. combinatoricsnumber theoryconsecutive