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.
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