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Putnam
1985 Putnam
A1
Putnam 1985 A1
Putnam 1985 A1
Source:
August 5, 2019
Putnam
Problem Statement
Determine, with proof, the number of ordered triples
(
A
1
,
A
2
,
A
3
)
\left(A_{1}, A_{2}, A_{3}\right)
(
A
1
,
A
2
,
A
3
)
of sets which have the property that(i)
A
1
∪
A
2
∪
A
3
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
,
A_{1} \cup A_{2} \cup A_{3}=\{1,2,3,4,5,6,7,8,9,10\},
A
1
∪
A
2
∪
A
3
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
,
and (ii)
A
1
∩
A
2
∩
A
3
=
∅
.
A_{1} \cap A_{2} \cap A_{3}=\emptyset.
A
1
∩
A
2
∩
A
3
=
∅.
Express your answer in the form
2
a
3
b
5
c
7
d
,
2^{a} 3^{b} 5^{c} 7^{d},
2
a
3
b
5
c
7
d
,
where
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are nonnegative integers.
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