### Brain Teasers

# Backwards Clock

With the death of Arthur Minit, the legendary country of MADADIA's only clock maker, no one else had much experience yet with making clocks. The new church of MADADIA had just been completed and a new clock was needed to fit into the bell tower. A clock was made by the locals, using the books of Arthur Minit as a guide.The newly made clock was officially put into use when it showed 6 o'clock. But soon it was noticed that the hour-hand and minute-hand had been interchanged and attached to the wrong spindles. The result was that the hour-hand moved with a speed twelve times higher than the minute-hand. When a clock maker arrived from another area, a remarkable thing happened: on the moment he inspected the clock, it showed exactly the right time.

The Question: If the clock started in the 6 o'clock position, then what was the first moment that it showed the correct time again?

The Question: If the clock started in the 6 o'clock position, then what was the first moment that it showed the correct time again?

### Answer

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.

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