MathDB

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.

Problem Statement