MathDB

The set

A=\{1,2,3,\cdots, 10\}

contains the numbers

1

through

10

. A subset of

A

of size

n

is competent if it contains

n

as an element. A subset of

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

Problem Statement