A man had a clock with an hour hand and a minute hand of the same length and indistinguishable. If the clock was set going at noon, what would be the first time that it would be impossible, by reason of the similarity of the hands, to be sure of the correct time? In grappling with this little problem, you may assume that it is possible to indicate fractions of a second. On this assumption, an exact answer can be given.

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THE SOLUTION

The first time would be 5 and 5/143 minutes past 12, which might also indicate 60/143 minutes past 1. Or, expressed slightly less accurately, 5 minutes past 12 and about half a minute past 1.