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IMO Longlists
1985 IMO Longlists
61
Maximal value of k
Maximal value of k
Source:
September 14, 2010
combinatorics unsolved
combinatorics
Problem Statement
Consider the set
A
=
{
0
,
1
,
2
,
…
,
9
}
A = \{0, 1, 2, \dots , 9 \}
A
=
{
0
,
1
,
2
,
…
,
9
}
and let
(
B
1
,
B
2
,
…
,
B
k
)
(B_1,B_2, \dots , B_k)
(
B
1
,
B
2
,
…
,
B
k
)
be a collection of nonempty subsets of
A
A
A
such that
B
i
∩
B
j
B_i \cap B_j
B
i
∩
B
j
has at most two elements for
i
≠
j
i \neq j
i
=
j
. What is the maximal value of
k
?
k \ ?
k
?
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