A Puzzle
Here’s a puzzle I came up with while working tech support at my very first job.
At 12:00 the hour and minute hands of a clock overlap. To the nearest second, what time is it when they next overlap.
There are two ways to solve this problem. If you understand the puzzle, it won’t take you long, but if you go at it the most obvious way, you may find yourself trapped in Xeno’s paradox.
daeguowl said,
August 30, 2007 @ 1:49 pm
So what’s the solution then?
LostRambler said,
August 30, 2007 @ 2:47 pm
What, and spoil it for everyone else?
daeguowl said,
August 31, 2007 @ 2:01 pm
Do you have the readers to justify that comment? Email me…
daeguowl said,
September 2, 2007 @ 8:06 am
Depends how many decimal places you want to go to….12 hours will have to elapse for it to be an exact overlapping (provided your watch is accurate). However, after one second, the hour hand will have moved 0.0083333 of a degree and the minute hand will have moved 0.01 of a degree whidh to the naked eye will be unnoticeable….at 4:21:49 and 7:38:11 the hands will overlap with a difference of 0.008333333 degrees which is the closest they’ll be during the twelve hour period.
LostRambler said,
September 2, 2007 @ 9:34 am
Given that at 3:10 the minute hand is above the hour hand and at 3:20 it’s below, there must be some time when they overlap between 3:10 and 3:20. This time occurs before 4:21, so your answer is at least one hour out.
And we’re talking about a mathematical overlap, one that is only true for an infinitessimally small period of time. We’re talking about a purely theoretical clock too, one on which the hands move smoothly and at a constant rate.
daeguowl said,
September 4, 2007 @ 4:31 pm
Then it comes about 1:06′27″ (can’t remember exactly….). As you said to the nearest second, the 40′clock one is where, to the nearest whole second, the hands are closet to each other. The overlapping at 1:06 has the being directly in the position half way through a second, and further apart at the start and end of that second, than at 4o’clock…
LostRambler said,
September 6, 2007 @ 6:16 am
Cool, you got the right answer, to the nearest second (as opposed to the answer that’s nearest to a whole second).
daeguowl said,
September 6, 2007 @ 2:15 pm
Do I get a prize>?