MICROSOFT Interview Puzzle:
CLOCK HANDS:
1.Question: How many times a day do the minute and hour hands of a clock
overlap?
Answer: 22 times a day
Did you think the answer was 24 times? Well if you did, it’s
time you think again. Let’s do some math.
In T hours, the minute hand completes T laps. In the same amount
of time, the hour hand completes T/12 laps.
The first time the minute and hour hands overlap, the minute
hand would have completed 1 lap more than the hour hand. So we have T = T/12 +
1. This implies that the first overlap happens after T = 12/11 hours (~1:05
am). Similarly, the second time they overlap, the minute hand would have
completed two more laps than the hour hand. So for N overlaps, we have T = T/12
+ N.
Since we have 24 hours in a day, we can solve the above equation
for N
24 =
24/12 + N
24 = 2
+ N
N
= 22
Thus, the hands of a clock overlap 22 times a day. Thus the
hands of the clock overlap at 12:00, ~1:05, ~2:10, ~3:15, ~4:20, ~5:25, ~6:30,
~7:35, ~8:40, ~9:45, ~10:50. Note that there is no ~11:55. This becomes 12:00.
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