Hamilton's Ireland

To mark the 175th anniversary of the October 1843 discovery of quaternions, last year, we suggested a "Hamilternion" card game based on quaternion multiplication.  (The 176th anniversary of quaternions is celebrated here.)

This year, to mark Maths Week 2019, we present a totally different and much easier game.  It's modelled after one that Hamilton himself invented over a decade after he came up with quaternions, and it's a great exploration of a key concept (the so-called icosian calculus) which he was the first to investigate.  (This is not relate to quaternions in any way!)

Consider the "map" below, featuring numerous places in Ireland associated with Hamilton.

Credit: "Casino image" created by Dan Bascelli based on an idea by Colm Mulcahy,

with content input from Anne van Weerden

Readers are invited to "retrace Hamilton' steps" by visiting all of these places associated with him, each one exactly once, using the "roads" shown, and returning to the starting location. 

For instance, let's start at Dunsink (the observatory and Hamilton's home), then proceed to Broom Bridge, TCD and RIA (Royal Irish Academy) in that order, just as we believe Hamilton himself did on a famous morning in 1843. 

Can you keep going, visiting everywhere else exactly once, before returning once more to Dunsink? 

Some roads might not be used at all, what is most important is to visit each location exactly once. 

A second question is,

Can it be done if you go to Nenagh immediately after RIA?

Have fun!  It might be worthwhile printing out the map and exploring the options with a pencil.

Anne van Weerden has kindly assembled information connecting each of the listed places to Hamilton.

Hint: there is an anagram above of the name of Hamilton's key invention.