Enigma 1694: The town clock prank
18 April 2012
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From New Scientist #2861, 21st April 2012 [link]
Our town clock has a standard 12-hour face, divided into 60 minute marks. The hands do not move smoothly: the minute hand moves sharply on to the next minute mark at the end of each minute, and the hour hand moves at the end of each 12 minutes.
The other day, a prankster swapped the hands (an operation that only took a few seconds between movements of the mechanism). Immediately after the swap, the clock showed the wrong time, but it was a valid time; in other words, the relative positions of the hands made sense. Within the next 10 minutes, the clock had shown the right time for exactly 2 minutes.
What time did the clock show immediately before the hands were swapped?