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Poland - First Round
1995 Poland - First Round
3
3
Part of
1995 Poland - First Round
Problems
(1)
Picking people from a group that know each other
Source: Poland Math Olympiad 1995 Round 1 #3
6/12/2023
In a group of
k
n
kn
kn
persons, each person knows more than
(
k
ā
1
)
n
(k-1)n
(
k
ā
1
)
n
others (
k
,
n
k,n
k
,
n
are positive integers). Prove that one can choose
k
+
1
k+1
k
+
1
persons from this group so that each chosen person knows all the others chosen.Note: If a person
A
A
A
knows
B
B
B
, then
B
B
B
knows
A
A
A
.