Collide the trains

posted by vibgyor
- July 26 2010 11:28:45 AM

There are two trains on a track o infinite length. There are two stations, say A and B. The distance between the stations is unknown. Also the original position of the trains is unknown. You can remotely drive the trains. You have the following controls at your hand:

1) You can move the train either forward or backward

2) You have a light indicator when a train comes to a particular station.

You are located at a very remote location from where you cannot view the trains, track or stations.

How can you make then collide?

1) You can move the train either forward or backward

2) You have a light indicator when a train comes to a particular station.

You are located at a very remote location from where you cannot view the trains, track or stations.

How can you make then collide?

Reply by kastashado
- August 11 2010 06:21:05 PM

you cannot because the tracks are infinite, direction was never given, there fore in either direction, they would never touch. infinite is infinite just as eternity is everlasting and never lasting.

Reply by kronk
- September 30 2010 02:20:18 AM

Okay, here's my train of thought (ha ha).

There are three possibilities for the direction:

A: x and y both face to the left (left being B->A)

B: x faces to the left, y to the right

C: both face to the right

I start by letting train x drive forward and y drive backward. After a certain amount of time (let's say 10 minutes) I reverse the direction of both trains and let them drive for 20 minutes, after that I reverse again and let them drive for 30 minutes, and so on.

With possibilities A and C they will collide sooner or later, no matter where they are regarding to the stations and how far apart they are.

So only for possibility B are the light indicators important, since they drive in the same direction if I control them as written above.

Now, here are three different possibilities regarding the position of the trains (x,y) relative to the stations (A,B):

1: x and y are both outside of A-B

2: x is outside, y is inside of A-B

3: x and y are inside of A-B

2 is also possible with y being outside, but it's the same case really, since I assigned x and y randomly.

At this point I made a sheet to cover all the possibilities, so here it is:

http://oi51.tinypic.com/2ngvkwm.jpg

There are three possibilities for the direction:

A: x and y both face to the left (left being B->A)

B: x faces to the left, y to the right

C: both face to the right

I start by letting train x drive forward and y drive backward. After a certain amount of time (let's say 10 minutes) I reverse the direction of both trains and let them drive for 20 minutes, after that I reverse again and let them drive for 30 minutes, and so on.

With possibilities A and C they will collide sooner or later, no matter where they are regarding to the stations and how far apart they are.

So only for possibility B are the light indicators important, since they drive in the same direction if I control them as written above.

Now, here are three different possibilities regarding the position of the trains (x,y) relative to the stations (A,B):

1: x and y are both outside of A-B

2: x is outside, y is inside of A-B

3: x and y are inside of A-B

2 is also possible with y being outside, but it's the same case really, since I assigned x and y randomly.

At this point I made a sheet to cover all the possibilities, so here it is:

http://oi51.tinypic.com/2ngvkwm.jpg

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