I have a clock at home that chimes on every hour and half hour mark. On whole hour marks it chimes once for each hour, and on half hour marks it chimes only once.
One night I was wakened suddenly and realized the the clock had chimed, but I did not know how many times. As I lay awake thinking about nothing in particular I heard the clock chime once and started wondering what time it was.
What is the longest amount of time I would have to lie awake before I knew for sure what time it was?
(In reply to
Puzzle Answer by K Sengupta)
Usually, at 1 o'clock or after, the individual will have to wait no more than one hour, since the clock will chime once at half hour and after half hour will certainly chime more than once.
This also holds true for any full hour starting at 2 o'clock when the clock will chime more than once followed by a single chime at half hour.
However, there are two exceptions:
CASE 1: The individual woke up precisely at midnight
In this situation, after precisely 30 minutes he will hear the clock chime once at 12:30 ( or 00:30 to be more precise) followed by the single chime at 1 o clock.
Then, he will be confused by the two single chimes and, would not be
able to ascertain the time.
He would therefore have to wait for the half-hour chime at 1:30, whence the three single chimes in 90 minutes would confirm the time as 1:30
CASE 2: THE individual woke up precisely at 12:30 (00:30 to be more precise)
Then the two successive single chimes at 1:00 and 1:30 will only confuse him since, in his mind the two chimes could very well occur at 12:30 and, 1:00. He would have to wait to listen to the 2 chimes sounding at 2:00 to be absolutely certain about the exact time.
Considering the two abovementioned cases, we are now in a position to assert that the longest amount of time the individual would have to stay awake before he knew what time it was IS 90 MINUTES,
Edited on May 17, 2022, 11:57 pm
Explanation to Puzzle Answer
