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MathNet 2020 — Math Olympiad Vault — Part 02 Question 53

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 02

Question 53

Partition the integers $1,2, \ldots, 8$ into sets $A$ and $B$. Let $P_{A}$ be the product of all elements of $A$ and $P_{B}$ the product of all elements of $B$.
What are the minimum and maximum values of $P_{A}+P_{B}$?

Note: The product over an empty set $E$ is defined as 1.