by Mark Valentine

Published Sunday October 18 2026 (link)

An AI app is learning to play a game of virtual darts. The board is a square, subdivided into nine squares. The resulting central square is divided in the same way, and the process continues ad infinitum.

The value of each outer square is 1. Each smaller square has the same constant prime multiple of the value of the next larger square. A dart landing in a given square scores the average value of all squares of the same size or smaller, weighted by area. Thus, the closer the dart lands to the centre, the higher the score.

At first, the app sometimes got a non-integer score, but after improving always got an integer score.

What was the non-integer score (as a fraction)?