MathDB

Let

A

and

B

be two non-empty subsets of

X = \{1, 2, . . . , 11 \}

with

A \cup B = X

. Let

P_A

be the product of all elements of

A

and let

P_B

be the product of all elements of

B

. Find the minimum and maximum possible value of

P_A +P_B

and find all possible equality cases.
Proposed by Greece

Problem Statement