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Turkey MO (2nd round)
2011 Turkey MO (2nd round)
1
Turkey NMO 2011 Problem1
Turkey NMO 2011 Problem1
Source:
December 7, 2011
symmetry
combinatorics unsolved
combinatorics
Problem Statement
n
≥
2
n\geq2
n
≥
2
and
E
=
{
1
,
2
,
.
.
.
,
n
}
.
A
1
,
A
2
,
.
.
.
,
A
k
E=\left \{ 1,2,...,n \right \}. A_1,A_2,...,A_k
E
=
{
1
,
2
,
...
,
n
}
.
A
1
,
A
2
,
...
,
A
k
are subsets of
E
E
E
, such that for all
1
≤
i
<
j
≤
k
1\leq{i}<{j}\leq{k}
1
≤
i
<
j
≤
k
Exactly one of
A
i
∩
A
j
,
A
i
′
∩
A
j
,
A
i
∩
A
j
′
,
A
i
′
∩
A
j
′
A_i\cap{A_j},A_i'\cap{A_j},A_i\cap{A_j'},A_i'\cap{A_j'}
A
i
∩
A
j
,
A
i
′
∩
A
j
,
A
i
∩
A
j
′
,
A
i
′
∩
A
j
′
is empty set. What is the maximum possible
k
k
k
?
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