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2022 JHMT HS
4
Range Contained in Subset
Range Contained in Subset
Source:
August 8, 2024
combinatorics
2022
Problem Statement
For a nonempty set
A
A
A
of integers, let
r
a
n
g
e
A
=
max
A
−
min
A
\mathrm{range} \, A=\max A-\min A
range
A
=
max
A
−
min
A
. Find the number of subsets
S
S
S
of
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
such that
r
a
n
g
e
S
\mathrm{range} \, S
range
S
is an element of
S
S
S
.
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