MathDB

A number of

n > m \geq 1

soccer teams play a full tournament, each team meeting (once) each other. Points are awarded:

2

for a victory,

1

for a tie and

0

for a loss. At the end, each team has won half of its points against the

m

teams placed last (including each of these teams, who won half of its points against the other

m-1

). Find all possible values for

n

and

m

, supported with examples of such tournaments.

2