Enigma 1774: March of the ants
6 November 2013
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From New Scientist #2942, 9th November 2013 [link]
A vertical piece of string is attached to a flat horizontal sheet of chicken wire, which forms a lattice of regular hexagons with 1-centimetre-long sides. The string is attached at one of the joints between three hexagons. Six ants marched down the string and along the wire, always moving further from their starting point on the wire. After a while, they had all marched the same distance along the wire (which was a whole number of centimetres less than 20 centimetres), but they were all at different straight-line distances from the starting point.
If I told you one of these straight-line distances, you would be able to calculate the straight-line distances the other five ants were from the starting point.
How far had the ants marched along the wire?