MathDB

Let

c \geq 4

be an even integer. In some football league, each team has a home uniform and anaway uniform. Every home uniform is coloured in two different colours, and every away uniformis coloured in one colour. A team’s away uniform cannot be coloured in one of the colours fromthe home uniform. There are at most

c

distinct colours on all of the uniforms. If two teams havethe same two colours on their home uniforms, then they have different colours on their away uniforms. We say a pair of uniforms is clashing if some colour appears on both of them. Suppose that for every team

X

in the league, there is no team

Y

in the league such that the home uniform of

X

is clashing with both uniforms of

Y

. Determine the maximum possible number of teams in the league.

Problem Statement