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The Chime Clock
Contributed by Andrew Kim

puzzle : chimer clock

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There is a clock that has a special way of telling the time. It does not have any hands or numbers on it, but it has a chimer.

If the time is 1 o'clock, it chimes once. If the time is 2 o'clock, it chimes twice, and so forth. The time gap between any two chimes is 3 seconds.

How many seconds would it take you to know the time, after the first chime is heard, if it is 6 o'clock?
Answer: 18

Solution:
If it is 6 o'clock, the clock will chime 5 times after the first chime is heard.
Since the time gap between any two chimes is 3 seconds, this will take 5 × 3 = 15 seconds.

Now, to know what time it really is, you have to wait an 'extra chime gap' to see if the clock chimes again.
Adding the extra 3 seconds, the total time required is 15 + 3 = 18 seconds.

Food for thought:

Does the solution assume that the time taken for the sound of the chime itself is negligible?

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