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 twelve 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?
And are there any other moments the clock will show the correct time?

Consider a good clock superimposed on this bad clock.  Each occupied hand position will have a good hand and a bad hand.  Regardless of which is the hour hand and which the minute hand, one will be going around at 2 rev/day and the other at 24 rev/day, a difference of 22 rev/day, so they (the good hand and the bad hand initially together) will meet every 1/22 of a day.  That's every 1440/22 minutes, or 65 5/11 minutes.

The times are therefore:

7:05  5/11
8:10  10/11
9:16  4/11
10:21  9/11
11:27  3/11
12:32  8/11
1:38  2/11
2:43  7/11
3:49  1/11
4:54  6/11
6:00

Edited on October 17, 2005, 10:41 am

Posted by Charlie on 2005-10-17 10:38:14