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expected value of square of triangle area, from lattice points in (0,0)-(4,4)

Source: Canada Repêchage 2024/5 CMOQR

March 25, 2024
expected valuegeometrycombinatoricslattice points

Problem Statement

Let S S be the set of 2525 points (x,y)(x, y) with 0≤x,y≤40\le x, y \le 4. A triangle whose three vertices are in SS is chosen at random. What is the expected value of the square of its area?
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