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King's Maths School

Challenge 436: Anton's Dodecagon

Anton the ant makes a journey around a dodecagon...

Anton is at vertex A of a regular dodecagon ABCDEFGHIJKL. He wishes to visit a number of vertices, always walking in a straight line. The following routes are available:

(1) The "Grand Tour" - Anton visits all 12 vertices in order.

(2) The "Big Tour" - Anton visits every 3rd vertex, i.e. D, G, J then back to A.

(3) The "Mini Tour" - Anton visits every 4th vertex, i.e. E, I then back to A.

(4) The "Micro Tour" - Anton visits every 6th vertex, i.e. G then back to A.

Anton considers either a Grand Tour followed by a Micro Tour, or a Big Tour followed by a Mini Tour.

Without using a calculator, find which option is longer.

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.