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Baltic Way
2007 Baltic Way
8
8
Part of
2007 Baltic Way
Problems
(1)
Non-isolated subsets
Source: Baltic Way 2007
11/30/2010
Call a set
A
A
A
of integers non-isolated, if for every
a
∈
A
a\in A
a
∈
A
at least one of the numbers
a
−
1
a-1
a
−
1
and
a
+
1
a+1
a
+
1
also belongs to
A
A
A
. Prove that the number of five-element non-isolated subsets of
{
1
,
2
,
…
,
n
}
\{1, 2,\ldots ,n\}
{
1
,
2
,
…
,
n
}
is
(
n
−
4
)
2
(n-4)^2
(
n
−
4
)
2
.
combinatorics proposed
combinatorics