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## Question

A clock chimes the hour, every hour on the hour, and once each quarter hour in between.

If you hear it chime once, what is the longest you may have to wait to be sure what time it is?

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A clock chimes the hour, every hour on the hour, and once each quarter hour in between.

If you hear it chime once, what is the longest you have to wait to be sure what time it is?

an hour and 45 min... it could pass through 1:00...

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an hour and 45 min... it could pass through 1:00...

Close, but not quite. It's an even better one!

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just 45 minutes, if it is one o'clock then you just heard a single chime, you would have to wait to see if you heard the double chime for 2 o'clock, if you get a single chime in 45 minutes then it must be 1:45

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If it updates itself for Daylight Savings time, then it could be 2 hours and 45 minutes if it chimed at 12:15am before the fall DST

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Assuming a normal day and not DST:

Perhaps you only heard the final chime of 12 o'clock. Then it would take 2 hours to get to 2 o'clock. To take your question literally though, the longest you have to wait is however long it takes the clock to chime more than once at a time =)

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as long as it takes you to get up and look at the clock

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Good thinking, but no one has it yet.

1:45 [jcalonego] is close, but not quite right.

45 minutes [finance_it] is quite a bit off, and makes a mistake about when the interval could start.

DST [GIJeff] doesn't figure in, because that change is made between 2:00 am and 3:00 am.

2:00 or how long it takes for the clock to strike more than once [itachi-san] is close, too, but not quite right.

Looking at the clock [finance_it] I guess is allowed by the OP, but I meant how long, just by listening. My bad.

If you hear it chime once, what is the longest you may have to wait to be sure what time it is?

Note: "may" inserted, here and OP, for clarity.

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IF time is 12:14, then next 7 chimes will be once. 8th will be 2 chimes. From 1215 to 145, that is 90 minutes, and if you hear all 7 chimes, you know it must be 145 as that's only way to have 7 consecutive single chimes. Answer is 90 minutes.

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A clock chimes the hour, every hour on the hour, and once each quarter hour in between.

If you hear it chime once, what is the longest you may have to wait to be sure what time it is?

12:00:01 - 14:00:00 could be the period. - though I have laid awake in the small hours listening to our dear old clock!

usually the quarters are different chimes therfore 1 sec less than 59mins if you missed the strike - I think.

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On the right track ... but from the OP you should be able to conclude

that you start the interval from a moment of a single chime. When

does the interval end, that will make the longest time you'd have to

wait until you're sure what time it is? Think about the time the interval

starts and how long you might wait until you're sure what time it is.

That's just a restatement of the OP, but it should show that some

guesses are going to be wrong, so I hope that's a help.

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Ok, I'm going to be stubborn and remain confident of my answer UNLESS some other time exists that applies to this one (but I have 99% ruled that out). I don't see how it can be anything LESS than my original answer, because if it were, then that force a possibly incorrect assumption on the starting time. Maximum consecutive single chimes is 7. I don't know how it could be any LONGER than my original answer unless you're pulling some daylight savings trick here

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A clock chimes the hour, every hour on the hour, and once each quarter hour in between.

If you hear it chime once, what is the longest you may have to wait to be sure what time it is?

If you can/are keeping track of the time, then if you happen to catch the last chime from the 12 o'clock hour then you would know your time at 12:15 since it will chime a few seconds (too lazy to be precise here) sooner than 15 minutes. The longest string of equally spaced single chimes is from 12:15 to 1:45. If you hear 5 chimes (since the initial chime), then the time could be 1:30 (originally 12:15) or 1:45 (originally 12:30). The next time the clock chimes it will either be one or two chimes. Right when the first chime happens, you still don't know the time, so you have to wait another second (<-assuming 1 second between chimes) to see if it is 2 or 1:45. So my answer would be 1 hour, 30 minutes, and 1 second.

If you are not keeping track of the time between chimes, then the last chime of the 12 for the 12 o'clock hour would be the first starting point and would add about another 15 minutes (but subtract some seconds due to the 12th chime being at 12:00:11) to the answer. My answer would then be 1 hour, 44 minutes, and 50 seconds.

Way off? Or did I get it?

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On the right track ... but from the OP you should be able to conclude

that you start the interval from a moment of a single chime. When

does the interval end, that will make the longest time you'd have to

wait until you're sure what time it is? Think about the time the interval

starts and how long you might wait until you're sure what time it is.

That's just a restatement of the OP, but it should show that some

guesses are going to be wrong, so I hope that's a help.

single chime is 12:15 - 12:30 is the interval so thats 15mins, unless it's 00:15 then I might drop off and not be certain unless i hear the second chime of 2am, but if the wife is down stairs changing the DST at the first chime (bless her) then it could be one more hour, Da6m it's 23:5 here. Hope I do not listen to the bells Esmerelda (that name rings a bell)

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...I don't know how it could be any LONGER than my original answer unless you're pulling some daylight savings trick here

Ahh...daylight savings does start at 2am, so that could add exactly another hour if that is what is being looked for.

If the clock malfunctions then you may need to wait until it is fixed. If the clock is never fixed, then you could wait indefinitely....or you could just give up listening to chimes and simply go ask someone for the time.

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Wow. It's not that hard. Really.

OK let's get the clutter out of the way.

[1] forget DST - say it's the middle of June.

[2] If you hear, say, the last chime of 12:00, you heard all 12 chimes.

Hmmm... I guess that's it.

Here's a hint.

One of EventHorizon's time intervals is correct, but the reason given

[start and end points] is not.

OK so now the answer should include the interval and the end points.

Final hint. No seconds are involved.

For the purpose of calculating intervals, you may assume every chime [however many

individual sounds it has] happens instantaneously on precisely :00, :15, :30, or :45.

There it is, on a platter.

Take it.

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1 hour 45 minutes. 12:15 - 2:00

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75 mins. largeneal was on the right track, but didn't properly eliminate all the possbilities:

Time: Possible Times

12:15: any quarter hour or 1

12:30: any :30, :45, 1:00, 1:15

12:45: any :45, 1:00, 1:15, 1:30

1:00: 1:00, 1:15, 1:30, 1:45

1:15: 1:15, 1:30 *

1:30: 1:30

For each successive ring, you only have to start with the previous possibilities.

*Edit: Oops. My bad. I somehow left 1:45 out as a possibility at 1:15, which means 1:30 could be 1:30 or 1:45, and you'd have to wait the full 90 minutes, as largeneal said. Ok, now I'm perplexed.

Edited by Duh Puck

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where is 1:45, though?

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you might not know the time that it chimes at. you would know how long you would have to wait, but only when you look at the clock would you know the time.

the amount of time you would have to wait could vary. if you don't look at the clock, then it would be a minimum of 15 minutes. usually it would be a 25 minute waiting period.

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largeneal has it.

My extreme bad for not reading back to previous page. post #7. :blush:

I have to say that the reasoning escaped subsequent posts.

largemeal correctly reasoned that at the 7th single chime you

know the time is 1:45.

[edit - the interval is thus an hour and a half]

You don't have to wait until the double chime at 2:00.

Thanks for bearing with my oversight, and congrats to largeneal!

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Haha - Bonanova - I love you, man - really, I do, because you come up with some great stuff. But goodness - I've been wondering all day how I missed that one!! Luckily I have a good therapist that helped me through the night :-P Nice puzzle

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...The longest string of equally spaced single chimes is from 12:15 to 1:45. If you hear 5 chimes (since the initial chime), then the time could be 1:30 (originally 12:15) or 1:45 (originally 12:30). The next time the clock chimes it will either be one or two chimes.

...

If you start at either 12:15 or 12:30, you still don't know what time it is after 6 chimes (1:30 and 1:45, respectively). After the sixth chime, if it is single then the time is now 1:45, and if it is double the time is obviously 2:00.

At either 12:15 or 12:30 it takes an hour and 30 minutes to determine what time it is. One you know because of too many single chimes and the other because the clock chimes twice.

There needs to be 2 possibilities before the last chime....or else there is nothing to disambiguate between.

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If you start at either 12:15 or 12:30, you still don't know what time it is after 6 chimes (1:30 and 1:45, respectively). After the sixth chime, if it is single then the time is now 1:45, and if it is double the time is obviously 2:00.

At either 12:15 or 12:30 it takes an hour and 30 minutes to determine what time it is. One you know because of too many single chimes and the other because the clock chimes twice.

There needs to be 2 possibilities before the last chime....or else there is nothing to disambiguate between.

If you're saying the answer is an hour and a half, you got it.

One shortfall of this puzzle is that 1:30 can refer both to a clock time and to the time interval.

I probably misinterpreted what you said.

What I was looking for is the observation that the longest possible string of single chimes is 7, and they span an hour and 30 minutes.

Or words to that effect.

Some answers were posted as a stream of consciousness thought flow and I may have not followed all of them correctly.

The catch is that some would reason you'd need to hear the two o'clock chime to be sure.

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Haha - Bonanova - I love you, man - really, I do, because you come up with some great stuff. But goodness - I've been wondering all day how I missed that one!! Luckily I have a good therapist that helped me through the night :-P Nice puzzle

Thanks.

Send me the therapist's bill.

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1h and 30min.In worst case you'll hear the clock at 12'45".After 7 chimes you'll know that is 13'45",because the next one will be for 2 o'clock.

A clock chimes the hour, every hour on the hour, and once each quarter hour in between.

If you hear it chime once, what is the longest you may have to wait to be sure what time it is?

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