MathDB

An (n, k) \minus{} tournament is a contest with

n

players held in

k

rounds such that:

(i)

Each player plays in each round, and every two players meet at most once.

(ii)

If player

A

meets player

B

in round

i

, player

C

meets player

D

in round

i

, and player

A

meets player

C

in round

j

, then player

B

meets player

D

in round

j

.
Determine all pairs

(n, k)

for which there exists an (n, k) \minus{} tournament.
Proposed by Carlos di Fiore, Argentina

Problem Statement