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2021 Cono Sur Olympiad
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2021 Cono Sur Olympiad
Problems
(1)
P3 Cono Sur 2021
Source: Cono Sur 2021 P3
11/30/2021
In a tennis club, each member has exactly
k
>
0
k > 0
k
>
0
friends, and a tournament is organized in rounds such that each pair of friends faces each other in matches exactly once. Rounds are played in simultaneous matches, choosing pairs until they cannot choose any more (that is, among the unchosen people, there is not a pair of friends which has its match pending). Determine the maximum number of rounds the tournament can have, depending on
k
k
k
.
combinatorics