# Detour: The Icosian Game

Explore a game that has Hamiltonian cycles in it.

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## 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.

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