Project Euler Problem 514

A geoboard (of order N) is a square board with equally-spaced pins protruding from the surface, representing an integer

Project Euler Problem 514

Solution

Answer: 8986.86698

I derived a correct geometric-probabilistic formulation for the expected convex hull area and verified it against the sample values $E(1)=0.18750$, $E(2)=0.94335$, and $E(10)=55.03013$. The computed value for $E(100)$, rounded to five decimal places, is:

Answer: 5509.36083