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27
2014 Guts #27: Maximum Value of Sum of Minima
2014 Guts #27: Maximum Value of Sum of Minima
Source:
August 26, 2014
Problem Statement
Suppose that
(
a
1
,
…
,
a
20
)
(a_1,\ldots,a_{20})
(
a
1
,
…
,
a
20
)
and
(
b
1
,
…
,
b
20
)
(b_1,\ldots,b_{20})
(
b
1
,
…
,
b
20
)
are two sequences of integers such that the sequence
(
a
1
,
…
,
a
20
,
b
1
,
…
,
b
20
)
(a_1,\ldots,a_{20},b_1,\ldots,b_{20})
(
a
1
,
…
,
a
20
,
b
1
,
…
,
b
20
)
contains each of the numbers
1
,
…
,
40
1,\ldots,40
1
,
…
,
40
exactly once. What is the maximum possible value of the sum
∑
i
=
1
20
∑
j
=
1
20
min
(
a
i
,
b
j
)
?
\sum_{i=1}^{20}\sum_{j=1}^{20}\min(a_i,b_j)?
i
=
1
∑
20
j
=
1
∑
20
min
(
a
i
,
b
j
)?
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