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## Question

Suman has a very lovely battery driven wall clock in her bedroom. Every hour a cuckoo comes out of the clock and sounded as many times as is the time at that hour in a very sweet voice. Cuckoo sounds every 15 minutes also but for once only. Five LED's of different colors are provided in a circle, at the middle of the clock. LED's glow whenever cuckoo sounds, making the clock looks very beautiful.

It was a daily routine of Suman to go to sleep at around 10:30 PM.

On a hot night, when she was in deep sleep, she woke up suddenly feeling hot. She wondered what happened to A.C. In the dark she tried to switch on the light, and then she came to know that power supply was not available. Suddenly she heard cuckoo sounding once, LED's also glowed for once and went off. She could not see what time it was and wondered what time it was.

She could not sleep due to heat, and had to wait for power supply to restore. After some time again the clock sounded once, LED's glowing for once, leaving Suman wondering how many times she has to listen the clock to know the exact time without seeing the clock.....?

Could anybody guess it for Suman....?

Edited by bhramarraj

## Recommended Posts

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Well, it depends. All beeps (or cuckoo's sound) will be for one time between 11PM and 2AM (assuming it sounds once at 00:00 just because 15 min completes that time too). After 2AM there will be 3 beeps every time (after 15 min each) before saying actual time. So, it depends on whether suman woke up between 11PM and 2AM or after 2AM. Also is there any significance of LEDs or they are just there to make question long and to confuse us?

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Questions:

1. Do I need to count the first cuckoo sound that she heard on waking up?

2. How many times does the cuckoo sound at midnight?

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I think the worst scenario would be that the first chime occurs at 12:45 am. If so, the next chime could be a quarter-hour or 1am, so could the next, etc., until 4 pass, at which point it could be 1am or later. At 12:45am, the 7th chime will be double, for 2am. So minimum 4, max 7.

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1 more will tell her the minute's 2 will tell her the hour

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6

12:15 First in puzzle

12:30 Second in puzzle

12:45

1:00

1:15

1:30

1:45

2:00

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Minimum 1 more if the last cuckoo was for the 45 min mark prior to any hour other than 1:00am. If the bird last sounding was for 12:30, then Suman will have to wait for the sixth sounding to determine that it is 2:00am.

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1-5 more cuckoos

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The worst case is if the first chime she heard was at 12:15 am, the chimes would be identical at 12:30, 12:45, 1:00, 1:15, 1:30 and 1:45. Until she heard the seventh chime she could not be sure of the time. She would not have to wait for the 2:00 chime in that case.

For her to wake at any time after 12:15 and before 1:00, she will hear the 2:00 chime in less than 7 intervals and know what time it is. Any time after 2 (or before midnight) and she will hear the hour by the fourth chime.

So she has to hear it a minimum of one more time and a maximum of five more times to know what time it is.

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There is two possible answer , 12:45 am or 1:15 am

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0 times...all she has to do is look at her cell phone.

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Well, it depends. All beeps (or cuckoo's sound) will be for one time between 11PM and 2AM (assuming it sounds once at 00:00 just because 15 min completes that time too). After 2AM there will be 3 beeps every time (after 15 min each) before saying actual time. So, it depends on whether suman woke up between 11PM and 2AM or after 2AM. Also is there any significance of LEDs or they are just there to make question long and to confuse us?

I am intrigued by your answer for it demonstrates such a different mindset with this digital age. All cuckoo clocks are 12 hour clocks, hence at midnight the clock reads 12:00 AM, not 00:00. Further evidence of these is the inclusion of bedtime referred to as 10:30 PM, not 22:00 as would have been the case for 24 hour time specification.

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I am intrigued by your answer for it demonstrates such a different mindset with this digital age. All cuckoo clocks are 12 hour clocks, hence at midnight the clock reads 12:00 AM, not 00:00. Further evidence of these is the inclusion of bedtime referred to as 10:30 PM, not 22:00 as would have been the case for 24 hour time specification.

Agreed. Unfortunately, I never had a cuckoo's clock.

But in that case, question is whether she woke up between 12 midnight and 2AM or after 2AM. From question both are possible and if it is the first case (between 12 midnight and 2AM), we cant determine a definite answer.

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Well, it depends. All beeps (or cuckoo's sound) will be for one time between 11PM and 2AM (assuming it sounds once at 00:00 just because 15 min completes that time too). After 2AM there will be 3 beeps every time (after 15 min each) before saying actual time. So, it depends on whether suman woke up between 11PM and 2AM or after 2AM. Also is there any significance of LEDs or they are just there to make question long and to confuse us?

LED's are just there just to confuse the reader. And at 00.00 it will sound 12 times.

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Questions:

1. Do I need to count the first cuckoo sound that she heard on waking up?

2. How many times does the cuckoo sound at midnight?

1. Yes.

2. 12 times. as clock always show 12:00 whether it is midnight or is noon.

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I think the worst scenario would be that the first chime occurs at 12:45 am. If so, the next chime could be a quarter-hour or 1am, so could the next, etc., until 4 pass, at which point it could be 1am or later. At 12:45am, the 7th chime will be double, for 2am. So minimum 4, max 7.

Congrats...! Right you are. Sometimes when we have very simple solution in front of us, we do not believe it...!

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The worst case is if the first chime she heard was at 12:15 am, the chimes would be identical at 12:30, 12:45, 1:00, 1:15, 1:30 and 1:45. Until she heard the seventh chime she could not be sure of the time. She would not have to wait for the 2:00 chime in that case.

For her to wake at any time after 12:15 and before 1:00, she will hear the 2:00 chime in less than 7 intervals and know what time it is. Any time after 2 (or before midnight) and she will hear the hour by the fourth chime.

So she has to hear it a minimum of one more time and a maximum of five more times to know what time it is.

you are right....!

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Well, if it if she is lucky, the next chime will be an hourly chime that she can work out the time from. If she is unlucky, she will have to wait for the next chime. That will be an hourly chime. However, if she is VERY unlucky, that hourly chime will be 1 o clock, which will be indistinguashable to a 15 minuite chime. However, she does know 1 thing from 4 single-chimes in a row: it must be one of the four of the following: 1:00, 1:15, 1:30, or 1:45. Worst case sinario: she has to wait another 45 minuites for she can be sure (not an until 2:00 because if it chimes once for 3 times after that, she knows that it must be 1:45 at the last chime) Or, if the LED's were bright enough she might just about see the time on it if she looks closely. She should have one of those watches that will light up if you press a certain button.

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