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National and Regional Contests
China Contests
China Team Selection Test
2023 China Team Selection Test
P2
P2
Part of
2023 China Team Selection Test
Problems
(1)
2023 China TST, Day 1, Problem 2
Source:
3/14/2023
n
n
n
people attend a party. There are no more than
n
n
n
pairs of friends among them. Two people shake hands if and only if they have at least
1
1
1
common friend. Given integer
m
≥
3
m\ge 3
m
≥
3
such that
n
≤
m
3
n\leq m^3
n
≤
m
3
. Prove that there exists a person
A
A
A
, the number of people that shake hands with
A
A
A
is no more than
m
−
1
m-1
m
−
1
times of the number of
A
A
A
‘S friends.
combinatorics
China TST