Time Stop
"Well, in that case, what time is it now?" asked the striker, noting that the wall clock said 2:00 PM.
"Time to be off," replied Chronos, picking up his cuckoo clock from the seat beside him and tucking it under his arm. "It's Thursday, and I have an appointment this afternoon in town. My seven-hour clock stopped this morning and I have to take it to the repair shop. Look it says 1:00 now." With this he swept out, making a timely exit.
When had the time stopped in his clock ?
"Time to be off," replied Chronos, picking up his cuckoo clock from the seat beside him and tucking it under his arm. "It's Thursday, and I have an appointment this afternoon in town. My seven-hour clock stopped this morning and I have to take it to the repair shop. Look it says 1:00 now." With this he swept out, making a timely exit.
When had the time stopped in his clock ?
Labels: logic, trickofmind
posted by Rajesh Lal at
12:33 PM
27 Comments:
1:00
Assuming Chrono's special 7-hour clock reads 7:00AM at what would normally be 12AM midnight every day. And every hour of Chrono's special 7-hour clock still has a base scale 60 minutes in every hour, and a base scale 60 seconds in every minute... Then Chrono's 7-hour watch keeps time at a 7/12 time scale, or for every hour that tick-by on Striker's normal watch only 35 minutes tick-by on Chrono's special 7-hour watch.
(Or a conversion of 7 divided by 12 = 0.58333.)
Then if Chrono's special 7-hour clock never stopped; his broken watch would be reading 1:10PM when Striker's normal 12-hour clock reads the current time of 2:00PM. (Or 1 hour and 10 minutes past noon. Noon being 7:00 hours on Chrono's special clock.).
Pictured more easily comparing a 24-hour clock to a 14-hour clock. If the 24-hour clock always reads 24:00 hours at midnight, and the 14-hour clock reads 14:00 hours at midnight. Then when the 24-hour clock reads the current time of 14:00:00 hours (2PM), then the 14-hour clock will read 08:10:00 hours (1:10PM).
Or in other words ---- 14.0 hours multiplied by 0.58333333 = 8.16666 hours. Where .166666 of an hour is 10 minutes. Again, 08:10:00 hours on a 14-hour clock, or, again, 1:10PM on a 7-hour clock face.
This means Chrono's 7-hour watch which is stuck on 1 (and he stated stopped in the morning) stopped working 7 hours and 10 minutes ago as read by his specal 7/14-hour watch.
Using the conversion above, 7 hours and 10 minutes ago in Chrono's special time equals 12.285714 hours ago in Striker's normal time. (7.166666 hours divided by the 0.58333333 conversion = 12.285714 hours)
12.285714 hours on a 12/24-hour clock is equivalent to 12 hours 17 minutes and 09 seconds. Chrono's watch stopped 12 hours 17 minutes and 09 seconds prior to the current standard time of 2PM, Thursday.
So, Chrono's watch stopped at 1:42:51 AM on Thursday morning. (Which is equivalant to the 1AM stuck on Chrono's special 7/14 hour watch.)
Time does not stop. It did not stop in his clock nor out of his clock. His clock may have stopped, but time did not.
If you are asking for a number, the answer is 42.
But you are forgetting that an hour is the same amount of time, whether on a 12-hour clock or a 24-hour clock. The only difference is how quickly the hands must move around the clock, not the time that elapses between hours.
So, assuming that at midnight the 7-hour clock reads 7:00 (or 0:00, which it would not every night since 7 doesn't go into 24 evenly) then at 7:00AM the clock would read 7:00 again, and when it reads 1:00 it would be 8:00 AM. Therefore the clock stopped "this morning", as the puzzle says, at 8:00 AM. If the clock had kept the correct time it would have read 7:00 again at 2:00PM.
I think both answers could be right, it just depends on how in the world a 7 hour clock works.
Anonymous above has made an error when stated "So, assuming that at midnight the 7-hour clock reads 7:00 (or 0:00, which it would not every night since 7 doesn't go into 24 evenly) then at 7:00AM the clock would read 7:00 again, and when it reads 1:00 it would be 8:00 AM.
A clocks first function is to display when a day (one full rotation of the Earth) has elappsed. This requires a clock - any clock - to return to it's starting point once during the day(same as the Earth rotates). Other wise it would not be a clock, at least not an accurate one.
It does not matter how many hours you break that rotation up into, or if "7 doesn't go into 24 evenly". There is no physical requirement that a planets rotation be broken into 24 segments. You can break a full day (rotation) into any number of segments you wish. So long as the hands come back strait-up to midnight at least once a day (rotation).
Turns-out, though, if you break your day (rotation) it into 14 segments (yeilding a 7-hour clock face), and you don't change the scale of minutes and seconds. Then one hour on a 7-hour clock face takes exactly 1 hour 42 minutes and 51 seconds on a 12-hour clock face. (Or, the reciprocal - one hour on a 12-hour clock face is the same as 35 minutes on a 7-hour clock.)
This 0.58333 "gearing" would bring the hands strait-up to midnight (the number 7 in this case) every night. Thus matching the Earth's rotation, and being an accurate 7-hour "clock".
the striker plays football now thats hard enough so leave me alone
An Earth clock should return to the same hour at sunrise (ignoring seasonal changes). Since and Earth day is 1440 minutes. Let's assume for simplicity a seven hour clock makes one full revolution a day (like a 24 hour clock), then if it is a Earth clock, each hour should be 1440 / 7 approx 205 minutes per hour. Or maybe 1/2 that if it makes two revolutions per day like a 12 hour clock.
I don't think this is a Earth Clock. Or maybe it a couple of billions of years in the past when Earth revolved much quicker,
Whoever is trying to state some weird gearing with .58333, please stop, you are being completely stupid. It is a 7 HOUR clock. Each time the hands go around, it equals one hour. It doesn't line up with the passage of one day.
If we assume that it starts at 0:00 (or 7:00) at midnight, It will read 1:00 one hour later, and also again eight hours later (and again at 15 hours later). So this leaves the options at 1:00, 8:00, or 3:00 (but it is only 2:00) so the answer is either 1:00 or 8:00.
This is a stupid question anyways because who has ever heard of a 7 hour clock, its stupid.
Why is everyone trying to say there is more than 60 minutes in an hour? It clearly states a 7 HOUR clock. We all know that there is 60 minutes in one hour. An hour is a set amount of time, that doesn't change because we are using a goofy clock.
Maybe Rajesh Lal will tell us all what he thinks the answer should be. There are several, which are correct and also wrong depending on your point of view.
A clearer question would benefit all of us.
Time, Stopped?
It is kind of like dividing by zero. If the time stopped, what does the question mean when it says "What time was it when time stopped.?" If it stopped yesterday, then today is still yesterday. If it's not yesterday, then time did not stop. If it DID STOP, then we must have reached infinity. See how it fits with dividing by zero?
It certaintly is a mind trick.
Thanks Rajesh
1:00 I Think
silly rabbit time doesnt stop
Monday.
-h
To all those idiots out there, the question CLEARLY states when did the time stop on his CLOCK. So anotherwords, the clock broke. NOT time in general has stopped. Try reading the question properly. All you who have said 'time has never stopped'... THATS NOT WHAT IT IS ASKING, YOU FOOLS!!!
If it doesn't match the rotation of the planet it is on...it is not a clock.
Minutes and seconds are measures of angels, not of time. (The reason for their base scales of 60 is due to the fact that a circular clock face has 360 degrees.) The amount of actual time "contained" in each minute, second (and hence hour) is totally arbitrary.
For a couple of years after the French Revolution the French time standard was a 10-hour clock. Also, in the 18th century the Italian's used a 6-hour clock. Each of these required a distinct "gearing" of the clock face to accomplish its job of keeping time.
12 (or 24) hours in a day are just as arbitrary. Little know fact - the number 12 is there to represent the 12 lunar cycles in the year.
Why does it matter?
People can just say it stopped at any time and they wont know if they are right or wrong.
Who cares.......
Chrono's watch stopped at 1:42:51 AM on Thursday morning.
Adieu...
Time had stopped in his clock at 1:00 AM that morning which is clearly mentioned in the question so there is no need of all those calculations
To above, it only states in the question that the clock said 1:00, meaning it either stopped at 1:00 or 7 hours later, at 8:00. so it is one of those two answers.
For those saying that an hour and minute isn't a set amount of time, please stop. A unit of time is a set amount of time, it is not dependent on what clock you are using, that's just stupid. An hour on my clock is the same as an hour on yours, no matter how many markings are on my clock. For a seven hour clock it will be 4 hours shy of making 4 rotations everyday. It doesn't change the amount of time in an hour, that's stupid.
Simply saying the clock stopped at 1AM is the epitomy of a "circular definition", and is not very illuminating.
(e.g. Q: What is a cellular phone? A: It is a "phone that is cellular".)
Making the calculation and converting to the commonly used duodecimal system of time keeping is a more complete answer.
So, if what Adam, above, is saying is correct when he says : ..." A unit of time is a set amount of time, it is not dependent on what clock you are using, that's just stupid. An hour on my clock is the same as an hour on yours"...Then the same logic would suggest one "degree" fahrenheit is the same as one "degree" centigrade. (i.e. one degree is a "set ammount" and it is the same on one scale as it is on another.)
But we know this is not true in both cases.
It's the same with counting time. Both measuring time and temperature are just systems of scaling. And while the measuring does not affect the underlying phenomenon being measured (time or temperature), what system of measuring you choose to use does affect the "number of units" (degrees or hours) you have as your final answer.
That is why 1:42:51 AM on a 12-hour clock is equivilant to 1AM on a 7-hour clock. Just the same as 32 DEGREES Fahrenheit is equilivant 0 DEGREES Centigrade. In both cases the same "amount" (heat or time) is being measured; just a different "number of units" is the final answer.
(Also, you seem to like using the word "stupid" a lot. I don't think anyone is forcing you to use that word. I believe you are choosing it voluntarily. Perhaps, that choice says more about you than it does about me... Yes? Maybe?)
The big difference you are omitting about your argument that makes it crucial, is that fahrenheit and celsius are two different scales. If you want to use a so called standard time scale and a non-standard time scale that has different amounts, that's fine, do that. You argument is like saying one degree celsius using my thermometer is different from one degree celsius on your thermometer because mine ranges from -20 to 130, and yours ranges from -40 to 160. One degree is the same on both of our thermometers, despite of the range on the thermometer.
Just because on my thermometer it rises 15 degrees (10%) doesn't mean it has to rise 10% on your thermometer, that's 20 degrees. They aren't the same. Units can't just be changed depending on how you measure them, they are concrete, just like a unit of time, it is also concrete.
So if you were to apply that CRITICAL piece of information, you'll see how your argument falls apart, there is only one scale for time, and two scales for temperature. And if you don't see that than I can't explain it anymore.
And at least I'm confident enough in my posts to put my name....
Anon #3, you mentioned the number 42. I just read a series of books called the Hitchhiker's Trilogy, even though there are more that three books. Anyway, the series is partly about the secret of "Life, the Universe, and Everything," which is apparently "42". Coincidence?
Adam, you're a little late to the party. The fact that 12-hour clock is a different SCALE than a 7-hour clock – is my answer, and was given quite a while ago. I am glad to see you are beginning to put that together. Now, the conversion between those two time scales is 0.58333. Just like the conversion between the scales of Centigrade and Fahrenheit is 1.8(+32 for the zero offset). Or the scales of kilograms to pounds is 2.21.
I am not sure, though, how your name being Adam (if that is your real name) makes your posts any more correct than mine. Unless, perhaps, you are implying that people named Adam are just inherently more correct than people not named Adam. Could you explain this argument - that posting your given name implies that you are more likely to be correct? I really would like to know how that works.
I can, however, say with great confidence that, in spite of all your sound and fury, you have provided no definitive answer of your own. I believe some posts previously you mumbled your position that the answer might fall within the hours of 1:00, 8:00 or 3:00. Since you did not specify AM or PM that gives you 6 possible hour-long answers in any 24-hour civil day...A one in four chance of being right. That's not bad odds for someone who now appears to be guessing. It is no wonder you now choose to hinge your ideas on statistical terms such as “confidence”. I was unaware this question required a “fiat” frame of reference.
On the other hand, I have provided an answer specific to the day of the week, hour, minute and second: Thursday at 01:42:51 AM. Given there are 604,800 seconds in any given week, I believe those odds of 1 in 604,800 should self-evidently imply the depth and scope of my confidence - the confidence you say I lack.
But I guess there is were the clarity lies...I now have a 1 in 604,800 chance of being correct. A person such as yourself - who simply proclaims that I am wrong and provides no answer of his own– now has a 604,799 in 604,800 chance of being right in stating that I am wrong. Saying that I am wrong – and providing no answer of your own – is the easiest position to take, covers the most bases, and takes the least amount of thought.
A good and obvious choice by you. But your answer (of my being wrong) is not what the original question was. Why don't you take a shot at that one for once...?
Apparently you haven't read my posts for more than a glance. I have stated that my answer is either 1:00 or 8:00 in multiple posts. I also said it could be 3:00 but it would be past the current time stated, so it couldn't. No I didn't say AM or PM because it was pretty obvious the time would have to be before 2 PM stated in the question. So that makes my answer (once again) either 1:00:00 AM or 8:00:00 AM.
How can there be a different scale for time? So if I measure someone running a race with a normal clock and the time is 6 hours, and you time another runner with your 7 hour clock and get 4 hours, did your runner finish the race faster? No, actually mine did, but the records would show yours did. Time is a constant, it can not be changed due to how you measure it. That's the big point you are missing. You can throw all sorts of numbers and math around and make it look fancy, but that doesn't change anything. I'm sure you are intelligent with all that math, that's why i'm surprised you think time can change just by using a different clock.
You say a lot of words, most of which are used to "fluff" up your speech/image, or attempt to bring down (falsely) my arguments. You stated I haven't given an answer, or an exact answer, and I did, repeatedly. You try to use my counterargument for two different temperature scales to your argument, when actually it is against your position. Your 1:604,800 calculation is also irrelevant. And stating that I am taking the easy way out by not providing an answer is completely wrong too, I'm definitely not just doing that, but you can say what you want, you have thus far already.
I'm sure you'll reply in a big long post of fluff repeating yourself 4 times in the same post (again) trying to make yourself look good. I'm sure you'll throw in tons of numbers and complicated calculations because numbers look smart. But as far as I go, I won't make another post because I have made my point, and logical people will see that. I'm not running away or hiding like you'll try to say, I have just made my point and have nothing further to say. So you can have the last post and make yourself feel good. I don't care, I won't be joining you in thinking that a unit of time can change depending on the clock I use.
Thanks Adam. You said that all with a lot of confidence. And nothing you said was stupid.
I am sorry though. All three of the answers you gave are incorrect.
The 7-hour clock stopped at 01:42:51 AM on Thursday.
Ta-Ta...
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