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MathNet 2020 — Math Olympiad Vault — Part 04 Question 56

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 04

Question 56

Hossna is playing with an $m \times n$ grid of points. She can draw segments between some of the points with the following conditions:
a. No two segments intersect except in points of the grid.
b. Each segment is drawn between two consecutive rows.
c. There is at most one segment between any two points.
Find the maximum number of the finite regions Hossna can create.