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ISI Entrance Examination
2015 ISI Entrance Examination
3
Sum of max element of subsets
Sum of max element of subsets
Source: ISI Entrance 2015
May 10, 2015
combinatorics
isi
Problem Statement
Consider the set
S
=
1
,
2
,
3
,
…
,
j
S = {1,2,3,\ldots , j}
S
=
1
,
2
,
3
,
…
,
j
. Let
m
(
A
)
m(A)
m
(
A
)
denote the maximum element of
A
A
A
. Prove that
∑
A
⊆
S
m
(
A
)
=
(
j
−
1
)
2
j
+
1
\sum_ {A\subseteq S} m(A) = (j-1)2^j +1
A
⊆
S
∑
m
(
A
)
=
(
j
−
1
)
2
j
+
1
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