Enigma 538: Rule of the road
24 February 2020
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From New Scientist #1690, 11th November 1989 [link]
I recently visited Ruralania with its five towns, Arable, Bridle, Cowslip, Dairy, Ewe, joined by one-way roads labelled high or low, as in the map:
The Ruralanian road system is very simple; if a driver is at one of the five towns then the systems says whether he or she is to leave that town by the high road, by the low road, or to stop in that town.
The system is determined by the fact that it must be possible to make a Grand Tour by starting at a certain town and driving round visiting all the towns and stopping at the final town, while always obeying the single Rule (X):
Take the high road if taking the low road and then obeying Rule (X) again, results in your car next being at A or E. Otherwise, take the low road if taking the high road and then obeying Rule (X) again, results in your car next being at C. Otherwise, stop in the town where you are.
What is the Grand Tour? (List the towns in order).