Three integers a, b and c satisfy both 0 ≤ a ≤ b ≤ c and

          abc + ab + ac + bc + a + b + c = 2023

What is the smallest possible value for a + b + c?

Solution: Add 1 to both sides and factor to get (a + 1)(b + 1)(c + 1) = 2024.

We pick a = 7, b = 10, and c = 22, so that a + b + c = 39.