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games in a tournament

Source: Mathematics Regional Olympiad of Mexico Southeast 2017 P2

October 24, 2021
combinatorics

Problem Statement

In the Cancun´s league participate 3030 teams. For this tournament we want to divide the 3030 teams in 22 groups such that:
<spanclass=′latex−bold′>1.</span><span class='latex-bold'>1.</span> Every team plays exactly 8282 games
<spanclass=′latex−bold′>2.</span><span class='latex-bold'>2.</span> The number of gamen between teams of differents groups is equal to the half of games played.
Can we do this?
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