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Sandy Wood
Brain Game: Hands in the Face
by Sandy Wood - October 30, 2008 - 6:30 AM

bloghead_braingames.jpg

I remember when digital watches first became affordable in the early 1980s. My dad grumbled that it wouldn’t be long before kids wouldn’t have to learn to tell time, and that day may come sooner than he imagined.

Over a single 24-hour day, how
many times do an analog clock’s
hour and minute hands point
to the exact same spot?

HERE is the solution.

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Comments (11)

  1. Hmmm… Where does that extra minute come from in the 3, 5,7, and 9 o’clock hour. Am I missing something, or is this wrong?

    posted by Brian on 10-30-2008 at 7:19 am

  2. it’s 24 not 22. you forgot ~11:58 or 11:59. it’s once an hour so if there are 24 hrs in a day then the hands will overlap 24 times.

    posted by grant on 10-30-2008 at 7:22 am

  3. O.k., I just got it (in partial thanks to Grant). The hands wouldn’t overlap at 11:55 and 12:00. This would make the minute hand have to zip around an hour in 5 minutes. That extra minute on the hours is really the accumulation of 2 half-minutes of the the odd hour and the even before it.

    posted by Brian on 10-30-2008 at 7:29 am

  4. Grant: It doesn’t take an hour between matches, but a tad longer than that — 1 and 1/11th of an hour… so by the time it’s happened 11 times in a 12-hour period, the hands are back where they were originally.

    posted by Sandy on 10-30-2008 at 7:39 am

  5. ahhh, i see now.

    posted by grant on 10-30-2008 at 7:48 am

  6. Will report back about this time tomorrow – just started counting…

    posted by Dan on 10-30-2008 at 11:05 am

  7. Shouldn’t the answer be 24, since the hour hand and minute will touch every hour?

    posted by NateJ on 10-30-2008 at 12:39 pm

  8. The extra minutes are simply where the hour hand is when the minute hand is sweeping around. Explained differently; by the time the minute hand reaches the 5 on the clock (25 minutes) where you would expect the hands to overlap the hour hand has moved closer to the six, putting it right around the 27 minute mark.

    posted by bristal on 10-30-2008 at 1:17 pm

  9. For those who think they should match once an hour, you’re right, except that it is at the very end of the 11 o’clock hour and the very beginning of the 12 o’clock hour. Essentially the same time. So the end of one 12-hour cycle overlaps the beginning of the next, so 22.

    posted by matt on 10-30-2008 at 1:54 pm

  10. Once an hour, the minute hand will pass over the hour hand at some time during that hour. It’s 24.

    posted by 24Slashing on 10-30-2008 at 2:19 pm

  11. There’s no time during the 11 o’clock hour (AM or PM) that the hands touch. They do at 10:56 or so, and then again at 12:00.

    That’s where the “missing two hours” come in.

    posted by Sandy on 10-30-2008 at 8:52 pm

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