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2013 Stanford Mathematics Tournament
22
22
Part of
2013 Stanford Mathematics Tournament
Problems
(1)
2013 General Problem 22
Source:
2/4/2013
The set
A
=
{
1
,
2
,
3
,
⋯
,
10
}
A=\{1,2,3,\cdots, 10\}
A
=
{
1
,
2
,
3
,
⋯
,
10
}
contains the numbers
1
1
1
through
10
10
10
. A subset of
A
A
A
of size
n
n
n
is competent if it contains
n
n
n
as an element. A subset of
A
A
A
is minimally competent if it itself is competent, but none of its proper subsets are. Find the total number of minimally competent subsets of
A
A
A
.