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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2012 India Regional Mathematical Olympiad
4
Similar to RMO 1997
Similar to RMO 1997
Source: RMO 2012
December 2, 2012
combinatorics unsolved
combinatorics
Problem Statement
Let
X
=
{
1
,
2
,
3
,
.
.
.
,
10
}
X=\{1,2,3,...,10\}
X
=
{
1
,
2
,
3
,
...
,
10
}
. Find the number of pairs of
{
A
,
B
}
\{A,B\}
{
A
,
B
}
such that
A
⊆
X
,
B
⊆
X
,
A
≠
B
A\subseteq X, B\subseteq X, A\ne B
A
⊆
X
,
B
⊆
X
,
A
=
B
and
A
∩
B
=
{
5
,
7
,
8
}
A\cap B=\{5,7,8\}
A
∩
B
=
{
5
,
7
,
8
}
.
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