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Posers and Puzzles

Posers and Puzzles

  1. 16 Jun '04 17:22 / 1 edit
    The time on my watch is exactly 12 o’clock. That is, the minute and hour hands are coincident. At exactly what time will they next be coincident?

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  2. Standard member Nemesio
    Ursulakantor
    16 Jun '04 18:10
    If the minute hand "ticks" into place every minute then:

    Every hour the hour hand moves 30 degrees, so every minute it moves 1/2 a degree. As there are 60 minutes in an hour, each minute that passes corresponds to 6 degrees (6*60=360). So, at 1:05 the minute hand will be at 30 degrees while the hour hand is at 32.5 degrees, and at 1:06 the minute hand will be at 36 degrees and the hour hand at 33 degrees. So it passes as it goes from 1:05 to 1:06 (during the "tick&quot.

    If the minute hand moves smoothly throughout the minute (rather than simply "ticking" into place the moment a minute has passed).

    Then, every second that passes corresponds to 1/60 of 6 degrees for the minute hand (1/10 degree) and every second that passes corresponds to 1/60 of 1/2 degree (or 1/120 degree). At 1:05 M=30, H=32.5. So to figure out how many seconds, solve for x:

    30+(x/10) = 32.5 +(x/120)
    =
    2.5=(x/10)-(x/120)
    =
    2.5=(11x/120)
    =
    x=27.27272727 etc.
    Plug in:
    (27.2727 * 1/10)+30=32.727272 degrees for the minute hand
    (27.2727 * 1/120)+32.5=32.727272 degrees for the hour hand.

    Nemesio
  3. 16 Jun '04 18:26
    Well done, nemesio.

    This event occurs 11 times in 12 hours.
    Therefore ir occurs once every 12/11 hours
    Hence required time is 60/11 minutes past 1 o'clock.

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  4. Standard member Otis
    Lucky Patzer
    18 Jun '04 06:56
    not a second later? Because my watch as a second hand. Or if the watch breaks at 12 then it will always be. Or I could just hand crank the hands to coincide any time I want
  5. 19 Jun '04 11:27 / 2 edits
    Originally posted by Otis
    not a second later? Because my watch as a second hand. Or if the watch breaks at 12 then it will always be. Or I could just hand crank the hands to coincide any time I want
    The question never mentioned a second hand. Clocks and watches don't need second hands.

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