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Canada National Olympiad
2021 Canada National Olympiad
3
3
Part of
2021 Canada National Olympiad
Problems
(1)
Canadian MO 2021 P3
Source:
3/12/2021
At a dinner party there are
N
N
N
hosts and
N
N
N
guests, seated around a circular table, where
N
≥
4
N\geq 4
N
≥
4
. A pair of two guests will chat with one another if either there is at most one person seated between them or if there are exactly two people between them, at least one of whom is a host. Prove that no matter how the
2
N
2N
2
N
people are seated at the dinner party, at least
N
N
N
pairs of guests will chat with one another.
combinatorics