Can you solve Faulty Clocks Puzzle? Logically Yours Mohammed Ammar
video description
Better to have a generalized solution, I think. I considered the 12-hour clock face as if it were a 720-minute face. That way you needn't consider the hour hand's position. 0 minutes and 720 minutes are equivalent positions, just as 0 hours and 12 are on a standard clock. Let each clock's minute hand position be a function of time, t. One can choose units for t as appropriate. In this case, since minutes gained/lost always fall on a whole hour, I used t in hours, but one could easily use minutes or even seconds if required. The hands' positions are given by:
ClockL(t) = 720 - t/18 because it loses 1 whole minute every 18 hours
ClockG(t) = 0 + t/6 because it gains 1 whole minute every 6 hours
To find when they show the same minute, set those equal to one another and do some quick algebra. Easy, and you can solve any similar problem very quickly just by plugging in the loss/gain rates. This has the added benefit of telling you the clock faces' value when they meet-which is a nice sanity-check on your math, too. Take your answer and divide by the rate for either clock and you will see the total minutes gained or lost before they sync. In this case, clock L loses 180 minutes (12 o'clock minus 3 hours) and G gains 540 minutes (12 o'clock plus 9 hours. When synced, they both show 9 o'clock.
Date: 2023-11-15
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Comments and reviews: 17
Arthur
Ok, just so my past algebra teachers know I learned something.
The clocks being analog should be irrelevant
60 minutes x 12 hours = 720 minutes
12 on a standard 12 hour clock is 0 minutes or 12 hours = 720 minutes.
Clock L loses 2 minutes in 36 hours or 2/3 of a minute in 12 hours
G gains 2 minutes in 12 hours
We can express the gains and loss within a 12 hour period as
L(i) = 720 minutes - 2i/3 minutes
G(i) = 0 minutes + 2i minutes
Where i is an increment by 1 minute starting at 0 and going to 270 (12 hour period.
The clocks are equal when L(i) = G(i)
270 minutes - 2i/3 minutes = 2i minutes
3(370 minutes - 2i/3minutes) = 3(2i minutes)
2160 minutes - 2i minutes = 6i minutes
2160 minutes = 6i minutes + 2i minutes
2160 minutes = 8i minutes
2160 minutes / 8 = 8i minutes / 8
270 minutes = i minutes
i = 270
because i is a 1-minute interval
i = 270 minutes / 60 minutes = 12 hours
For a visual, if you graphed the two functions they should intersect at i=270
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Ok, just so my past algebra teachers know I learned something.
The clocks being analog should be irrelevant
60 minutes x 12 hours = 720 minutes
12 on a standard 12 hour clock is 0 minutes or 12 hours = 720 minutes.
Clock L loses 2 minutes in 36 hours or 2/3 of a minute in 12 hours
G gains 2 minutes in 12 hours
We can express the gains and loss within a 12 hour period as
L(i) = 720 minutes - 2i/3 minutes
G(i) = 0 minutes + 2i minutes
Where i is an increment by 1 minute starting at 0 and going to 270 (12 hour period.
The clocks are equal when L(i) = G(i)
270 minutes - 2i/3 minutes = 2i minutes
3(370 minutes - 2i/3minutes) = 3(2i minutes)
2160 minutes - 2i minutes = 6i minutes
2160 minutes = 6i minutes + 2i minutes
2160 minutes = 8i minutes
2160 minutes / 8 = 8i minutes / 8
270 minutes = i minutes
i = 270
because i is a 1-minute interval
i = 270 minutes / 60 minutes = 12 hours
For a visual, if you graphed the two functions they should intersect at i=270
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DESTROYED
I wrongly interpret your questions many times. in this question, I didn't know that you meant 12 o clock when you said -the same time-. I thought -the same time- as the duration when both clocks shows coinciding time, which means same hours & same minutes.
In this case, the answer is 11days 6hours & 45 minutes (from the moment the clocks started. At this point, both clocks will show 6hrs 45 minutes. AM or PM depends on when the clock started.
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I wrongly interpret your questions many times. in this question, I didn't know that you meant 12 o clock when you said -the same time-. I thought -the same time- as the duration when both clocks shows coinciding time, which means same hours & same minutes.
In this case, the answer is 11days 6hours & 45 minutes (from the moment the clocks started. At this point, both clocks will show 6hrs 45 minutes. AM or PM depends on when the clock started.
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DavidS
You lose 40s = 1/90hr on L clock and gain 2 min = 1/30h on the G clock, for each 12-hour cycle. The L time is moving backwards and the G time is moving forwards, so the place they meet is what you want.
If x represents a 12-hour cycle,
then 12 - (1/90)x = 0 + (1/30)x.
12 = (4/90)x
x = 270 12-hour cycles, so 3240 hrs.
But your answer is much simpler.
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You lose 40s = 1/90hr on L clock and gain 2 min = 1/30h on the G clock, for each 12-hour cycle. The L time is moving backwards and the G time is moving forwards, so the place they meet is what you want.
If x represents a 12-hour cycle,
then 12 - (1/90)x = 0 + (1/30)x.
12 = (4/90)x
x = 270 12-hour cycles, so 3240 hrs.
But your answer is much simpler.
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Jessica
Woohooo an old person puzzle, this I can do! - I suspect the trickiest part of this for youngsters is how unfamiliar an analogue clock feels to many of them, and remembering it shows the same time every 12 hours. It's funny how many everyday items are being replaced by better, even the concept of clocks losing/gaining time is becoming ye olde school now lol -
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Woohooo an old person puzzle, this I can do! - I suspect the trickiest part of this for youngsters is how unfamiliar an analogue clock feels to many of them, and remembering it shows the same time every 12 hours. It's funny how many everyday items are being replaced by better, even the concept of clocks losing/gaining time is becoming ye olde school now lol -
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Araqius
We can assume that clock L show correct time while clock G gains 8 minutes every 36 hours (= 8 minutes every 2, 160 minutes.
Clock L travel speed is 2160/2160 = 1. -
Clock G travel speed is 2168/2160. -
S(1) + 720 = S2-
t + 720 = 2168/2160 - t-
720 = 0. 0037037037037037037037037037037 - t-
t = 194, 400 minutes = 3, 240 hours.
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We can assume that clock L show correct time while clock G gains 8 minutes every 36 hours (= 8 minutes every 2, 160 minutes.
Clock L travel speed is 2160/2160 = 1. -
Clock G travel speed is 2168/2160. -
S(1) + 720 = S2-
t + 720 = 2168/2160 - t-
720 = 0. 0037037037037037037037037037037 - t-
t = 194, 400 minutes = 3, 240 hours.
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Josh
You made it much to complicated. The simple solution is, The total amount of minutes in 12 hours is 720, as we know, every 36 hours the clocks approache each other by 8 minutes, if so we devide the total amount of minutes by 8 (720/8 = 90. All that is left to do is multiply this by the rate of change 90-36 = 3240. Thats it.
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You made it much to complicated. The simple solution is, The total amount of minutes in 12 hours is 720, as we know, every 36 hours the clocks approache each other by 8 minutes, if so we devide the total amount of minutes by 8 (720/8 = 90. All that is left to do is multiply this by the rate of change 90-36 = 3240. Thats it.
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Anush
It can be same time with in 12 hrs, coz For the first 12hrs there is no change in both the clocks, L loses after 36 hours, and G gains after 12 hrs. So with in the first 12 hrs both clocks show same time. just sharing if am wrong plz correct me.
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It can be same time with in 12 hrs, coz For the first 12hrs there is no change in both the clocks, L loses after 36 hours, and G gains after 12 hrs. So with in the first 12 hrs both clocks show same time. just sharing if am wrong plz correct me.
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trigonzobob
I guess it wasn't needed, but I first determined that clock L will lose 3 hours and clock G will gain 9 hours the next time they read the same - L/(L+G)= 1/4 and 1/4 of 12 is 3. It takes clock L 3-60/2-36 = 3240 hours to lose 3 hours.
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I guess it wasn't needed, but I first determined that clock L will lose 3 hours and clock G will gain 9 hours the next time they read the same - L/(L+G)= 1/4 and 1/4 of 12 is 3. It takes clock L 3-60/2-36 = 3240 hours to lose 3 hours.
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Rajat
This was too easy of a puzzle. I really miss your old tough puzzles such as the 5 pirates modified one. Plz sir make some videos on tough puzzles. I really appreciate your efforts and videos. Great work.
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This was too easy of a puzzle. I really miss your old tough puzzles such as the 5 pirates modified one. Plz sir make some videos on tough puzzles. I really appreciate your efforts and videos. Great work.
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Ryan
Yeah. Working it out in minutes would have been so much easier. I converted everything to seconds. I came out wit the same final answer, but I had to work out the arithmetic with bigger numbers.
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Yeah. Working it out in minutes would have been so much easier. I converted everything to seconds. I came out wit the same final answer, but I had to work out the arithmetic with bigger numbers.
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dino
They will meet a 9 o'clock if started from 12 o'clock 9 hours
9 hours have 540 mins divided by 2 = 270 mins ( 12 hours increase 2 mins or 1 minute in 6 hours and 540 mins in 540 -6 ) ie 3240
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They will meet a 9 o'clock if started from 12 o'clock 9 hours
9 hours have 540 mins divided by 2 = 270 mins ( 12 hours increase 2 mins or 1 minute in 6 hours and 540 mins in 540 -6 ) ie 3240
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nimesh
Dear sir i think if one clock gains time and Another clock looses time then they should show same time in under 12 hrs unless you count am and pm as in digital clocks
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Dear sir i think if one clock gains time and Another clock looses time then they should show same time in under 12 hrs unless you count am and pm as in digital clocks
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David
I really enjoy your videos. well done! They all involve some great problems, and understanding the solution methods expands our abilities in general. Thanks so much!
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I really enjoy your videos. well done! They all involve some great problems, and understanding the solution methods expands our abilities in general. Thanks so much!
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Prathamesh
In 36 hr
8 min diff
In 36-7. 5
1 hr diff
In 36-7. 5-12
Diff is 12hr
Therefore ans
After 3240 hrs times are same: )
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In 36 hr
8 min diff
In 36-7. 5
1 hr diff
In 36-7. 5-12
Diff is 12hr
Therefore ans
After 3240 hrs times are same: )
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Salim
Ammar sir,
After 270 hrs both the clock will show same time of 11. 45
Ur answer takes longer time-
PLZ REPLY IF CORRECT OR CORRECT ME
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Ammar sir,
After 270 hrs both the clock will show same time of 11. 45
Ur answer takes longer time-
PLZ REPLY IF CORRECT OR CORRECT ME
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Sudeeshna
12: 01(or rather the next millisecond) itself they both show the same time right? Since to loose / gain minimum time required is 12 hrs.
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12: 01(or rather the next millisecond) itself they both show the same time right? Since to loose / gain minimum time required is 12 hrs.
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UTKARSH
It's actually not a tough problem, but it seems to be very tough when you get in competitive exams; thanx sir for a very simple approach.
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It's actually not a tough problem, but it seems to be very tough when you get in competitive exams; thanx sir for a very simple approach.
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