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1999 Harvard-MIT Mathematics Tournament
5
1999 Advanced Topics #5: Sum of Subsets
1999 Advanced Topics #5: Sum of Subsets
Source:
June 21, 2012
Problem Statement
For any finite set
S
S
S
, let
f
(
S
)
f(S)
f
(
S
)
be the sum of the elements of
S
S
S
(if
S
S
S
is empty then
f
(
S
)
=
0
f(S)=0
f
(
S
)
=
0
). Find the sum over all subsets
E
E
E
of
S
S
S
of
f
(
E
)
f
(
S
)
\dfrac{f(E)}{f(S)}
f
(
S
)
f
(
E
)
for
S
=
{
1
,
2
,
⋯
,
1999
}
S=\{1,2,\cdots,1999\}
S
=
{
1
,
2
,
⋯
,
1999
}
.
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