PRIZE PUZZLE FOR SEPTEMBER 2008
Two ordinary (analogue) 12-hour clocks, A & B, are set to the correct time of day. Clock A loses one minute every hour. Clock B gains 30 seconds every hour. How long will it take the two clocks to show the same time again? Is this time the correct time of day?
The answer is 480 hours or 20 days. And NO, when that happens they do NOT show the correct time.
Work it out this way: clock A loses 15 minutes every hour compared with clock B and for this to become zero it is necessary that this difference must mount up to 12 hours, because ordinary clocks cycle over 12 hours. So we must divide 12 hours by 15 minutes per hour which is 480 hours. After this time, clock A will be 480 minutes slow and clock B will be 240 minutes fast (which is the same thing) compared with their original settings. This is 8 hours slow (or 4 hours fast) so the correct time is four hours wrong and we would have to wait 60 days for both clocks to show the correct time again.
I received only two answers to this problem, both correct. One was from Richard Birkhill and the other was from John Stafford. This response was insufficient to warrant a draw but I hope it was fun solving the problem!