Suppose that a second pair of hands turns together with the wrong pair
of hands, but then in the correct way. When the wrong pair is in the
same position as the correct pair, this means that the time is shown in
the right way. First look at the hour-hands that are at the twelve. One
turns with the correct speed, the other with a speed that is twelve
times as small. These two hands are in the same position again when the
'slow' hand has progressed x minutes. The fast hand then has progressed
60+x minutes. For the time x that passed, then holds: (60+x)/12 = x.
This means that x = 5 5/11 minutes.
For the minutes-hands that start at six holds the same. The confused clock therefore shows the correct time again at 5 5/11 minutes past 7.
For the minutes-hands that start at six holds the same. The confused clock therefore shows the correct time again at 5 5/11 minutes past 7.
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