SMT 2023 Discrete Tiebreaker #2
Source:
May 3, 2023
Problem Statement
Every cell in a grid of paper is to be painted either red or white with equal probability. An edge of the paper is said to have a "tree" if the set of cells depicted in the diagram below are all painted red when the paper is rotated so that the edge lies at the bottom. Given that at least one edge of the paper has a tree, what is the expected number of edges that have a tree?
https://cdn.artofproblemsolving.com/attachments/1/2/f81d8da53d7bc6819fc1dfe4acb9567d545856.png