Detour: The Icosian Game

What is the icosian game?

We make an historical detour to Dublin, with the creation in 1857 of the icosian game by the Irish mathematician William Hamilton. This “game”, which was a commercial flop, consisted of a wooden board with twenty pegholes and some lines connecting the holes, as well as twenty numbered pegs (see the figure below). The objective was to place the numbered pegs in the holes in such a way that peg 1 would be connected by a line on the board to peg 2, which would in turn be connected by a line to peg 3, and so on, until finally peg 20 would be connected by a line back to peg 1. In other words, if we follow the lines on the board from peg to peg in ascending order, we reach every peg exactly once and then arrive back at our starting peg.