MathDB

Let

n

be an integer greater than

1

and let

S

be a finite set containing more than

n+1

elements.Consider the collection of all sets

A

of subsets of

S

satisfying the following two conditions : (a) Each member of

A

contains at least

n

elements of

S

. (b) Each element of

S

is contained in at least

n

members of

A

.
Determine

\max_A \min_B |B|

, as

B

runs through all subsets of

A

whose members cover

S

, and

A

runs through the above collection.

Problem Statement