Solving a Locomotive Dilemma: Step-by-Step Guide

[chawki]

Homework Statement

The picture shows the unfortunate situation in which two locomotive drivers found themselves. The trains are driving in opposite directions on the same track.
The only aid is one short spur line. It can take one engine or one wagon at a time. There is only one engine and one wagon in each train. Both ends of the engine can be hooked on a wagon. A wagon can be hooked in both ends, of course either on another wagon or on an engine

Homework Equations

How can they pass each other?
How would you advise the locomotive drivers? Please draw a step by step solution.

The Attempt at a Solution

the wagon from the train on the right stays on the track while the engine of the same train goes to the spur line, then the train on the left goes forward and hooked the wagon which is still on the track...

 

[gneill]

The wagons are empty and identical, so the drivers exchange places. Ha!

 

[chawki]

think again...they didn't give all those information for nothing...

 

[SammyS]

Chawki, do you know the solution?

 

[erok81]

Can one of of the trains drop a wagon off and leave it?

i.e. can the white train leave its wagon where it is and then park in the spur. Of course and the end of the transition, it will pick it back up.

If so it should only take 4-5 trades.

 

[SammyS]

Only two of objects ever need to park on the spur: the black locomotive, then the black wagon.

 

[chawki]

Chawki, do you know the solution?

i don't know the solution, but you can see what i said when trying to find it...

 

[ashishsinghal]

the attempt by OP seems reasonable...

 

[chawki]

This is tricky...the end should be with white train on the LEFT and black treain on the RIGHT.

 

[chawki]

Can one of of the trains drop a wagon off and leave it?

i.e. can the white train leave its wagon where it is and then park in the spur. Of course and the end of the transition, it will pick it back up.

If so it should only take 4-5 trades.

Your idea is great...Yes it can

 

[chawki]

the attempt by OP seems reasonable...

what is OP?

 

[SammyS]

what is OP?

OP: Original Post 0r Original Poster

 

[chawki]

Ok sammy, anyway..after long day thinking about it..i found the solution..i will scan in soon

 

[chawki]

took me all day :shy:

 

[SammyS]

took me all day :shy:

Excellent! I mean the solution is excellent!

My solution was:

Spoiler

1. Black Locomotive leaves its wagon on the main track and then parks itself on the spur.
2. White Locomotive with its wagon moves forward attaching to the black wagon and making sure the white wagon clears the spur.
3. Black Locomotive pulls out of the spur and down the main track far enough so the White Locomotive can complete the next step.
4. White Locomotive with black wagon attached backs down the main track until the black wagon clears the spur. (White Locomotive is also pushing the white wagon.)
5. White Locomotive pushes the black wagon onto the spur, leaving it there, then backs onto the main track.
6. White Locomotive with white wagon proceeds on to its destination.
7. Black Locomotive backs onto spur to retrieve the black wagon, then proceeds on.

A picture is worth a thousand words - or so.

 

[chawki]

Yes yes sammy, your way is better, shortcut of mine :P
because there is no need to put the black wagon in the spur.. it will just add more steps...
but well...what a day... if i didn't find the solution today ..i would possibly dream about it tonight XD

 

[SammyS]

chawki,

Here's the picture. I still think you did a very good job. There are other solutions with quite a bit more shuffling.