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Your grandma’s wall clock chimes the appropriate number of times at
every whole hour, and also once every 15 minutes. If you hear the wall
clock chime once, how much more time do you need to figure out what the
time is, without looking at it?
This is the way to figure out the exact time!
Source
What was the challenge?
Since the clock chimes appropriate number of times at every whole hour, it's not difficult to predict the exact time after counting sounds but the exception of 1:00 AM/PM.
For example, if the first sound you heard at 4:30 AM then you will hear another sound at 4:45 AM and clock will strike 5 times at 5 AM by which you will easily know the exact time. So, even if you heard it at 15 minutes past any hour, you will need only 45 minutes to figure out the exact time.
But at 1:00 AM/PM the clock will strike only once & there the problem starts.
In worst condition, if you have heard first sound at 12:15 then clock will strike once for next 6 times at 12:30, 12:45, 1:00, 1:15, 1:30, 1:45. That is you will hear clock strike once for 7 consecutive times. So in worst condition, you need 1 hour and 30 minutes to figure out the exact time.
And if you hear the single strike for less than 7 consecutive times, then you can easily figure out the exact time.