MathDB

There are

300

participants to a mathematics competition. After the competition some of the contestants play some games of chess. Each two contestants play at most one game against each other. There are no three contestants, such that each of them plays against each other. Determine the maximum value of

n

for which it is possible to satisfy the following conditions at the same time: each contestant plays at most

n

games of chess, and for each

m

with

1 \le m \le n

, there is a contestant playing exactly

m

games of chess.

Problem Statement