Enigma 409: Hands and feet
11 August 2017
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From New Scientist #1559, 7th May 1987 [link]
There are six footpaths through our extensive local woods, one linking each pair of four large oaks. I decided to go on a long walk starting at one of the oaks, keeping to the footpaths, ending back where I started, covering each of the footpaths exactly twice, and never turning around part-way along a path.
Whenever I was at an oak my watch showed an exact number of minutes, and in the previous 30 seconds up to and including arriving at the oak or in the 30 seconds after leaving the oak the hour and minute hands of the watch were coincident.
I set out sometime after 6am and I was back home before midnight on the same day. I walked at a steady pace from start to finish.
What time was I at the oak at the start of my round walk, and what time did I get back there at the end of the day?