MathDB
Math Prize 2021 Problem 9

Source:

September 19, 2021
Math Prize for Girlsgeometry

Problem Statement

Let HH be a regular hexagon with area 360. Three distinct vertices XX, YY, and ZZ are picked randomly, with all possible triples of distinct vertices equally likely. Let AA, BB, and CC be the unpicked vertices. What is the expected value (average value) of the area of the intersection of ABC\triangle ABC and XYZ\triangle XYZ?