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55 replies to this topic

### #41 thoughtfulfellow

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Posted 20 September 2011 - 01:16 AM

The time at each loop is ONE minute also...
The spaces between trains are always equall...that means,,all the trains depart at the same time(as if they are connected together).
The time needed to travel between each two stations is ONE minute...
Each train stays one minute in each station.
and again....one train comes to the station...stays one minute...as it leaves the station,another train reachs it...stays one minute,and will leave it.....4 minutes after that there is no train.and then the process will be repeated again as mentioned above.
The train at station 24 will stay there one minute...then it will make a one minute loop,and returns back to this station(24),the same is true for the station number 1.
I hope it is clear now...

Let me again explain part of the problem with your scenario. You clearly state here that a train arrives from left at station 24. Here let me set my stop watch to 0:00. Next event train leaves this station into loop at the same moment a train arrives from the loop heading back to the left, stop watch reads 0:01. Train traverses the loop and again arrives at the station, stop watch reads 0:02. This would put the train spacing heading to the left at 1 minute. Note also that the train that arrived at 0:01 from the loop had to leave station 24 at 0:00, the moment that a train arrived from the left so that train, too, would be at 1 minute intervals. A similar problem occurs at the loop to the left of station 1 with this train spacing. Before the problem can be solved, this conflict in times must be addressed.
Summarizing: At station 24, 0:00 train 'A' arrives from left, 0:01 Train 'B' arrives from right(out of loop) & train 'A' exit station to the right into the loop, 0:02 Train 'A' arrives from the right. Position of train 'B' at 0:00 had to be leaving station 24 into the loop.
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### #42 thoughtfulfellow

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Posted 20 September 2011 - 01:38 AM

You are right. I didnt add the second 23*2. It is indeed 95 mins and 19 trains then.

When I saw 1 problem with yours, I did not examine further but just noticed you also skipped 1 minute stay at station 24 after train transverses loop. Another way to look at it. Since there are 24 stations and train stops at each twice, this is 48 stops with 48 spaces between stops, 96 intervals. Now the problem only comes to rationalizing what the loop time must be to meet all criteria. Assuming we were not told that a train arrives from the right at the same time a train leaves the station heading right. Then at station 24, the time between the train leaving the station and arriving to head the other way is the loop time. If we made the assumption that the loop time was 1 minute, then a train arrives from the right 2 minutes after it arrives from the left but we were told that this should only be 1 minute. If we are allowed to change this time interval to 2 minutes, then indeed it is an elementary problem and the answer would be 96/4=24 trains.
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### #43 wolfgang

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Posted 20 September 2011 - 06:00 PM

When I saw 1 problem with yours, I did not examine further but just noticed you also skipped 1 minute stay at station 24 after train transverses loop. Another way to look at it. Since there are 24 stations and train stops at each twice, this is 48 stops with 48 spaces between stops, 96 intervals. Now the problem only comes to rationalizing what the loop time must be to meet all criteria. Assuming we were not told that a train arrives from the right at the same time a train leaves the station heading right. Then at station 24, the time between the train leaving the station and arriving to head the other way is the loop time. If we made the assumption that the loop time was 1 minute, then a train arrives from the right 2 minutes after it arrives from the left but we were told that this should only be 1 minute. If we are allowed to change this time interval to 2 minutes, then indeed it is an elementary problem and the answer would be 96/4=24 trains.

As you mentioned above...there are 48 stops....and if there are 24 trains(as you think),so they should be(train........train......train.....)and that means there will be no interval between the trains arriving the station number 12..
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### #44 14.swapnil.14

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Posted 28 September 2011 - 10:36 AM

C:\Documents and Settings\Swapnilkale\My Documents\My PicturesI think that the post does'nt make sense
At 10:00 a.m.........a train arrives the station( from the left side).
at 10:01 a.m.........a train arrives the station( from the right side).
at 1005 a.m..........a train arrives the station( from the lsft side).
at 10:06 a.m..........a train arrives the station(from the right side).
and so on.........
All the staions are equally spaced,all the trains have the same speed,
and the time needed between any two stations is one minute.

Considering forward and backward line...
Since at the back line train will arrive at each station every 4min.
But the same is not true for forward line.(5min difference)
Since the forward and backward paths are connected via a 1min distance(same as distance between each station)
there is no solution(illogical)[speed of train and distances being same].

So i think on the forward line the difference in arrival should have been 3 min.
This will ensure the sync.
So at a given time each station would contain a train.
For instance trains at even stations would travel in forward direction
And trains at odd station would travel in backward direction.
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### #45 Trainspotterx

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Posted 01 October 2011 - 02:15 AM

Key here is each train only stops in each station for one minute. Therefore as it goes through journey it does not always stop.

Assume train leaves 12 at 10:01 after stopping for 1 minute and next arrives at 10:05 then this second train has been travelling for 4 minutes since it last stopped. A minute ago it was at 11 and a minute earlier 10. A further minute earlier at 9 where it passed through and minute earlier at 8 where it stopped

So at 10 train b arrives at 8
10:01 b leaves 8
10:02 b passes 9
10:03 b passes 10
10:04 b passes 11
10:05 b stops at 12

Thus when a is at 12, we have another at 8,4,16,20 - 5 trains. There is also one more at 1 which next stops at 4, and another at 24 about to head back after it's outward loop.

In each case on the line going the other way is train passing through except for 1 and 24.

In total this gives 12 trains.

Accordingly a train follows this order 4,8,12,16,20,24,21,17,13,9,5,1,3,7,11,15,19,23,22,18,14,10,6,2,4

Or something like this
10:03 b passes 11
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### #46 thoughtfulfellow

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Posted 01 October 2011 - 06:49 AM

I was sitting in a subway station No. 12(toatal stations are 24).
On this line are several trains transporting passengers from staion(No. 1 ) till the end station( No. 24),then each train will continue the journey from side to side(both sides are connected together at each end).I noticed that after each 4 Minutes a train arrives this station from left side toward the right side,one minute later another train arrives the station but to the opposit direction,and so on.
If each train stays in each station exactly one minute( notice that the train at each end will make a curve and return back to that staion,just like a circle).
Howmany trains are there on this line?

Key here is each train only stops in each station for one minute. Therefore as it goes through journey it does not always stop.

Assume train leaves 12 at 10:01 after stopping for 1 minute and next arrives at 10:05 then this second train has been travelling for 4 minutes since it last stopped. A minute ago it was at 11 and a minute earlier 10. A further minute earlier at 9 where it passed through and minute earlier at 8 where it stopped

So at 10 train b arrives at 8
10:01 b leaves 8
10:02 b passes 9
10:03 b passes 10
10:04 b passes 11
10:05 b stops at 12

Thus when a is at 12, we have another at 8,4,16,20 - 5 trains. There is also one more at 1 which next stops at 4, and another at 24 about to head back after it's outward loop.

In each case on the line going the other way is train passing through except for 1 and 24.

In total this gives 12 trains.

Accordingly a train follows this order 4,8,12,16,20,24,21,17,13,9,5,1,3,7,11,15,19,23,22,18,14,10,6,2,4

Or something like this
10:03 b passes 11

I do like your theory; however, it goes against the original stated problem which I have quoted above. Note the line that reads:
"If each train stays in each station exactly one minute( notice that the train at each end will make a curve and return back to that staion,just like a circle)"
Note that he says "each train" but by your method, some trains don't stay in station one minute and would violate the "each" part.
Also, examining your solution closer, you have trains stopping at station, skipping 3 stops, then stopping except at the end turnarounds. Remember from 24, train goes back to 24 (skips), 23 (skips) 22 (skips) and 21 keeping pattern, then at the nest end 1 back to 1 (skips), 2 (skip) then stop on 3 breaking your pattern. You then break your pattern again at the low end before returning to sta 4 after skipping 4 stops. Interestingly, these error due cancel out each other. so that the corrected order wold become:
4,8,12,16,20,24,21,17,13,9,5,1,4
You have also omitted the information about second train arriving from right 1 minute after the arrival of train from left. If we go by your theory of non-stops, then your 12 trains needs to be adjusted to account for those stopping in opposite direction and some explanation as to why stations 2,3,6,7,10,11,14,15,18,19,22,23 have no trains stopping. Assuming these are not redundant stations, then train number derived must also be doubled. Note those coming in from left with same pattern would mess up pattern from left when circling back and trains that do not follow the pattern are subject to causing collisions.
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### #47 Trainspotterx

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Posted 01 October 2011 - 03:27 PM

Fair point - it was too late when went for first attempt.

If each train stops once only at each station then when it stops at one it loops back but does not stop so therefore you have at each end two consecutive journeys without a stop.

Consider the train arriving at 1 from 2. It waits 1 minute and travels the loop in next minute, importantly does not stop and takes third minute to arrive at 2. It waits for a 4th minute travels for 1 minute to arrive at 3 after 5. And so until it arrives at 24 after 47. Minute 48 it sits at 24. Minute 49 it loops to 24 but does not stop and minute 50 it arrives at 23, 52 at 22 and so on until arrives back at the beginning after 94 minutes.

The only question now is what the gap is between trains. The problem is not clear so perhaps someone can clarify but based on this I would be guessing something like 19 trains.

I am late for something so hopefully someone can fill in what I have missed.
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### #48 Trainspotterx

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Posted 02 October 2011 - 10:42 AM

Fair point - it was too late when went for first attempt.

If each train stops once only at each station then when it stops at one it loops back but does not stop so therefore you have at each end two consecutive journeys without a stop.

Consider the train arriving at 1 from 2. It waits 1 minute and travels the loop in next minute, importantly does not stop and takes third minute to arrive at 2. It waits for a 4th minute travels for 1 minute to arrive at 3 after 5. And so until it arrives at 24 after 47. Minute 48 it sits at 24. Minute 49 it loops to 24 but does not stop and minute 50 it arrives at 23, 52 at 22 and so on until arrives back at the beginning after 94 minutes.

The only question now is what the gap is between trains. The problem is not clear so perhaps someone can clarify but based on this I would be guessing something like 19 trains.

I am late for something so hopefully someone can fill in what I have missed.

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### #49 Trainspotterx

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Posted 02 October 2011 - 10:55 AM

Okay so I assumed 94 minute round trip but stopping at stations going both directions except 1 and 24.

If they stop at every station for 1 minute only then I need to remove 22 minutes from the loop.

If we are to treat the trains at equal gaps then we need to divide 72 minutes into Segments.

Wolfgang - your time gap example skipped 6:02
which leads us to 7 minute gaps. Restating this
makes it 6 minute gaps.

Thus we have 12 gaps between trains.

Because it is loop we therefore 12 trains.
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### #50 wolfgang

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Posted 02 October 2011 - 06:30 PM

Okay so I assumed 94 minute round trip but stopping at stations going both directions except 1 and 24.

If they stop at every station for 1 minute only then I need to remove 22 minutes from the loop.

If we are to treat the trains at equal gaps then we need to divide 72 minutes into Segments.

Wolfgang - your time gap example skipped 6:02
which leads us to 7 minute gaps. Restating this
makes it 6 minute gaps.

Thus we have 12 gaps between trains.

Because it is loop we therefore 12 trains.

The 6 min. gap is correct...but the number of trains is not

Edited by wolfgang, 02 October 2011 - 06:32 PM.

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