Answer Posted / venkat
The answer is twenty-three.
Most people quickly realize that the answer has to be
twenty-four, give or take. The issue is nailing down
that "give or take" part. Recognize, first of all, that
there is nothing capricious about the overlaps. Both hands
move at fixed speeds.
Therefore, the time interval between overlaps is a
constant. This constant interval is a little more than an
hour. At midnight, the hour and minute hands are exactly
superimposed. It takes an hour for the minute hand to make
a complete circuit In that same time, the hour hand has
moved 1/12 of a circuit to the numeral 1. It then takes
another five minutes for the minute hand to catch up to
where the hour hand was, in which time the hour hand has
crept a bit farther.... Before getting sucked into a Zeno's
Paradox, let's settle for the moment by saying that the
interval is a little more than sixty-five minutes. We also
know that the exact interval has to divide evenly into
twenty-four hours, since the day ends as it started, with
both hands up and overlapping. In fact, it has to divide
evenly into twelve hours. The way the hands move in the
P.M. is an exact replay of the way they move in the A.M.
Focus on the twelve-hour period from midnight to noon. The
hands cannot overlap twelve times in that period, for if
they did, it would mean that the interval between overlaps
was 12/12, or exactly one hour — and we know it's a bit
more than sixty-five minutes. No, there must be eleven
overlaps in a twelve-hour period. That means the interval
between overlaps is 12/11 hour, which comes to 65.45
minutes. This must be the precise interval that we balked
at calculating a moment ago. Doubling eleven gives twenty-
two overlaps in a twenty four- hour period. Twenty-two is
the answer — unless you want to split hairs. Should you
count the overlap at the midnight that begins the day, and
also at the midnight that ends the day, the answer is
twenty-three.
| Is This Answer Correct ? | 43 Yes | 52 No |
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