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National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2023 Bulgaria JBMO TST
4
4
Part of
2023 Bulgaria JBMO TST
Problems
(1)
Subsets of 3 without exactly one common element
Source: 2023 Bulgaria JBMO TST Problem 4
5/7/2023
Given is a set of
n
≥
5
n\ge5
n
≥
5
people and
m
m
m
commissions with
3
3
3
persons in each. Let all the commissions be nice if there are no two commissions
A
A
A
and
B
B
B
, such that
∣
A
∩
B
∣
=
1
\mid A\cap B\mid=1
∣
A
∩
B
∣=
1
. Find the biggest possible
m
m
m
(as a function of
n
n
n
).
combinatorics
set
Subset