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A4/B5
A4/B5
Part of
2020 Princeton University Math Competition
Problems
(1)
2020 PUMaC Combinatorics A4 / B5
Source:
1/1/2022
Let
P
P
P
be the power set of
{
1
,
2
,
3
,
4
}
\{1, 2, 3, 4\}
{
1
,
2
,
3
,
4
}
(meaning the elements of P are the subsets of
{
1
,
2
,
3
,
4
}
\{1, 2, 3, 4\}
{
1
,
2
,
3
,
4
}
). How many subsets
S
S
S
of
P
P
P
are there such that no two distinct integers
a
,
b
ā
{
1
,
2
,
3
,
4
}
a, b \in \{1, 2, 3, 4\}
a
,
b
ā
{
1
,
2
,
3
,
4
}
appear together in exactly one element of
S
S
S
?
combinatorics