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Part of 1979 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1979 Problem 1.1

Source: Bundeswettbewerb Mathematik 1979 Round 1

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teams in a football league. During a championship, every two teams play exactly one match, but no team can play more than one match in a week. At least, how many weeks are necessary for the championship to be held? Give an schedule for such a championship.

combinatoricsfootball

Problem-3(last problem)

Source:

The plane is painted in red or blue color. Prove that you have a rectangle with the corners of the same color.