When the Swiss didn't have so much experience yet with making clocks, a painful mistake was made with a church clock. The 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 axes.

The result was that the hour hand moved with a speed precisely 23 times higher than the minute hand. When the clock maker arrived, a remarkable thing happened: on the moment he inspected the clock, it showed exactly the right time again.

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

(In reply to Question? by Kenny M)

My assumption is that we only know the relative speeds of the 2 hands and not the absolute speed of either which suggests there might be multiple solutions.  Thus if one finds the first instance of a valid time, it should be possible by scaling the absolute speed to make that valid time also an accurate time.

Posted by Larry on 2023-04-28 11:03:16