Clock Chime
A tick-tock clock chimes every hour on the hour, and once each quarter hour in between. If we hear it chime once, what is the longest we may have to wait to be sure what time it is?
Labels: logic, mathemagic, trickofmind
posted by Rajesh Lal at
9:17 PM
22 Comments:
1 hour and 45 mins
It chimes once at 12:15, then once for every next 15 mins until 2:00.
It takes 15 mins until 12:30, then another 15 mins until 12:45, then another 15 mins until 1:00, then another 15 mins until 1:15, then another 15 mins until 1:30, then another 15 mins until 1:45, then another 15 mins until 2:00.
15 mins + 15 mins + 15 mins + 15 mins + 15 mins + 15 mins+ 15 mins = 105 mins which is 1 hour and 45 mins
I'll change my answer:
It's 45 mins Coz at 12:45 it chimes, then at 1:00 (45 mins later) the chime will have gone 4 times and then you can be certain it is 1:00
I make it 1 hour and 30 minutes (90 minutes).
The longest you would have to wait is for 7 chimes in a row to be sure of the time.
If you hear the clock chime at 12:15, on the 7th chime you can be sure that the time is 1:45.
If you hear the clock chime at 12:30, on the 7th and 8th time you can be sure that the time is 2:00.
So the longest you will have to wait is 1 hour and 30 minutes (90 minutes).
You'll never know what time it is unless you knew what time it was when it started chiming and you've counted since then, but the question doesn't say when it starts chiming.
The clock might break...
anonymous 1 - I'm presuming the clock chimes the correct number of hours every hour, so at 3:00 it will chime 3 times etc.
So for most times you wouldn't have to wait more than 45 minutes if you hear it chime once as you would know when it chimed more than once on the hour.
If it's around 1:00 it would only chime once on the hour and every 15 minutes so it gets trickier.
anonymous 2 - clock could break, meteor might strike, your mum might call you to come home for dinner...
Assuming that we can be sure that we initially heard exactly one chime (i.e. there is no doubt that we did NOT hear the only the last chime, say, at noon): after the one chime, you may hear at most 6 more one-chimes, followed by two chimes, at 15 minute intervals, if it was 12:15, or a total of 1 hour and 45 min. You need to be able to distinguish this from 12:30, where you would hear 5 more one-chimes followed by two chimes (over the next hour and a half). The distinction can be made after 6 15-minute periods, based on whether you hear one or two chimes, so an hour and a half is needed: then you can say it was 12:15, if one chime is heard, or 12:30, if two chimes are heard.
If the original assumption is incorrect and you could have heard the last chime at noon as the only chime, slightly less than 15 minutes needs to be added to the answer, but this seems less likely in any real scenario.
Answer: 90 minutes.
What I think is the longest I have to wait to find out the right time is 15 mins. as it chimed once so it means it quarter of an hour which could be 12:45. and the question says that it chimes on every hour and chimes once on every quarter hour so I think on every hour it chimes according to the hour. So my explanation would be 15 mins maximum wait in order to find out the right time.
With the assumption that on the hour it chimes a number of times based on the time, ie if its 2o'clock it will chime twice, then the longest time it would take to be sure, would be for the period from 12:15 to 2:00.
At 12:15, 12:30, 12:45, 1:00, 1:15, 1:30 and 1:45, it would only chime once, so you could not be sure what time it is, but at 2:00 it would chime twice and that would tell you exactly what time it is now.
So 1 hour and 45 minutes is the LONGEST time you would have to wait to make sure.
Actually pramsay13 is correct i believe as the most number of single chimes in a row you can have is 7. So you would not have to wait for the 8th one which would be twice to know the time
The longest amount of time you would have to wait may actually be 104 minutes or 1 hour and 44 minutes. This will assume that you were waiting a maximum of 14 minutes prior to the initial chime. The longest sequence of single chimes is 7 (12:15 - 1:45). Once the 7th chime is heard you would know that it is exactly 1:45. Therefore 1 hour 30 minutes plus 14 minutes = 104 minutes.
"If we hear it chime once, what is the longest we may have to wait to be sure what time it is?"
Therefore maximum time is 1 hour 30 minutes and the earlier 14 minutes or so is irrelevant.
There are three diff Answers. Each is correct, in a sense…
1) "Surge" said it all. At 12:15, u heard 1 chime. Aft that, you heard 6 more 1-chimes. 15 mins later, you hear 2 chimes at 2:00. So, the total lapse time is:
(6 x 15 mins) + 15 mins = “1 hr - 45 mins” –
This can be considered as the commonly-acceptable and approx Answer (1h 45m)…
2) However, pls allow me to finish what "Surge" has left over:
a. At 12:00, each of 12 chimes strikes every 1 sec.
b. At the end of 12:00'11", u walked into the house, and heard the “last strike of 12 chimes”.
c. From there on, 14 mins and 48 secs later, u heard "2nd 1-chime" at 12:15.
d. 1 hr-45m later, at 2:00, you finally hear the 2-chime.
3) Final announcement by “JPL Rocket Scientist Gary Shark”:
a. Counting the initial-time you heard between 12:00'11" and 12:00'12",
b. Refer to 2c.
c. See 2d.
d. Counting the end-time you hear between 2:00’0” and 2:00'2",
e. Total Count-Down b4 our Apollo takes off:
1sec + 14m 48s + 1h 45m + 2secs = “1 hour 59 mins 51 seconds”.
This should be the mathematically-correct Answer (1h 59m 51s).
4) Gary’s boss, the “Senior Rocket Scientist WebUser” would then comment:
a. “ JPL computer had already calculated for the max count-down of 1h 59m 51s.”
b. “Therefore, once the clock strikes at 1:45, we can predict that the next strike will be 2-chime at 2:00.”
c. ““ Hence all above smart TrickOfMind Riddle-Readers will know precisely at 1:45’1”: it’s the longest possible time-lapse.“”
1sec + 14m 48s + 1h 30m + 1 sec = 1 hour 44 mins and 50 secs.
This is the practical and logically-correct Answer (1h 44m 50s).
Shark
Shark, there are a few flaws with your answer.
1) you've made a big assumption that the chimes will start on the hour, rather than the last one striking on the hour.
2) for someone to be out of earshot of the chimes, but one second later be able to hear them is almost impossible and you would have to take into account someone thinking "did I really hear that - did I hear another one before but didn't realise what I was hearing until I heard it properly" - (anyone that has done a hearing test will recognise this scenario)
Your suggestions 2 and 3 could never be right, because either way you wouldn't have to wait until 2:00 as the chime at 1:45 would always be the clincher, it's then only about whether you think it is possible that someone could hear the last chime but miss the previous one, which I think isn't possible so 1 is right.
Another scenario - it would be perfectly reasonable to assume that any normal clock would play a tune or equivalent every hour to deliberately distinguish hours from quarter hours, so the perfectly logical and correct answer in that scenario would be 45 minutes.
15 minutes
Pramsay13, the 14 minutes prior to the hour and a half are important in the fact that it is longest amoun of time one would have to wait in order to determine what time it was. This assumes that we don't start listening on the initial chime at 12:15 but at the point the 12 oclock chimes had stopped. Also assume that the sounds don't continue to reverberate after the 12th chime.
So, I enter a room that can't see the clock but can only hear the chimes. I must hear the 7th chime in order to tell the time. If the initial chime started at exactly the time I was placed in the room then 1 hour and 30 minutes would be correct, but I could've waited the additional 14 minutes prior to the 1st chime as well which makes it 104 minutes long.
Therefore, it is relevent to the maximum length of time one would have to wait to determine the time based on single tone chimes.
Id say look at the clock....who cares how many times it chimes idk about you but i learned how to read a clock in elementary school
i'd say at the most it should take you 30 seconds to look at the clock after you hear it chime to figure out what time it is.
It takes you 30 seconds to look at a clock and figure out what time it is? (remember SMALL hand tells you the number of hours)
anonymous 3 posts previous (it'd be good if you guys left a name so I know who to berate) - the 14 seconds are irrelevant as the question says "If we hear it chime once..." so even if you walk into a room in between chimes and have been in the room for 1hr 44 mins, you can discount the time before you hear a chime ergo 1hr 30 mins is the longest time you may have to wait.
Well if u dont know what time it is u will stand their listening to it chime till ur dead, cause those chimes r telling u what time it is, it's only telling u it's been 15 minutes since the last chime. so if u dont know when u started u will never know what time it is. just make a sun dial? or something idk.
Ok so if it is 1:15 the chimes go off then 1:30 the chimes go off again. So my answer is every 15min. Every quarter is 15 min. Theres 4 quaters in an hour. So you know its been 15 min since the last chime went off. It makes sence to me.
forever......
it might run out of battery.
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