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# MATHS WEEK: Try today's puzzle and explore some new cities

Can you figure this one out?
Oct 16th 2015, 11:15 AM 19,938 25

MATHS WEEK IS well underway with the country celebrating all the great things about algebra, trigonometry, probability and calculus.

Each morning, we’ve been setting you a puzzle to test your mathematical mettle. It’s all part of the drive to improve Ireland’s numeracy skills – and remember it’s never too late.

(If numbers absolutely terrify you, take a trip to the website where you’ll find more information and help).

Let’s get to Friday’s puzzle:

William Rowan Hamilton was Ireland’s greatest mathematician. (He even has his own stamp).

He was Andrews Professor of Astronomy at Trinity College and Royal Astronomer for Ireland therefore he lived at Dunsink Observatory which is just on the city side of the M50 between the Blanchardstown and Finglas exits.

On walking into town along the Royal Canal to preside at a meeting of the Royal Irish Academy he had an epiphany. He had been working for years on the challenge of multiplying three dimensional numbers and the solution came to him while passing Broombridge in Cabra.

This was on the 16 October 1843 – a day now known as Hamilton Day – in maths circuits. The RIA celebrates Hamilton day with a public lecture and Maynooth University organise a walk in Hamilton’s footsteps every year.

Maths Week Ireland includes Hamilton Day every year.

Hamilton was a child prodigy reputedly speaking 12 languages by the age of 12. He amused himself with a game he invented called the icosian game. It used a dodecahedran (not an icosohedron) which is a solid with 12 faces. All the faces are regular pentagons so it is one of the special platonic solids.

Hamilton imagined all the corners as cities and the edges where the faces meet as route between the cities. The challenge is to start at one designated city and travel through all cities finishing in a second designated city. The rules – and of course there has to be rules –  is that you can only travel by the routes and you can’t visit any city twice. Such a route is called a Hamiltonian path and is important in many practical applications.

The playing board depicted here does just as well as the dodecahedron. In fact it could be a dodecahedron squashed right down. You might be able to see that it is made up of 12 pentagons with a city marked with a letter on each intersection. Can you find a Hamiltonian path starting at City A and finishing at City B?

Hamilton’s Icosian Game

Check back tomorrow, same time of 11.15am, for the answers and for Saturday’s puzzle.