# The exchange station problem

This is a practical problem to illustrate the difficulties of railway workers in the period in which trains were in their early childhood, before the introduction of double tracks, automatic detours or roundabouts of wagons.

Yes, friends, we will travel back in time to the time of our brave grandparents, familiar with the recent arrival of the iron horse, to whom I dedicate this riddle, along with the good woman who illustrated me with this problem based on her own experience. Next, I will tell you the story just as she told it to me:

We had just arrived at the exchange station, where the trains intersect, when we realized that the southern express was broken. I think the reviewer commented something that the chimney had overheated and collapsed, so the locomotive had been stopped.

The image shows the southern express with its damaged engine (at the bottom of the image) and the approach of the northern express that had to cross the station to continue its path crossing with the broken train.

The problem is finding a way for both trains to cross. It is understood that it is not possible to use ropes, pulleys, flying detours or any other kind of tricks. It is a train crossing puzzle in which the objective is to ensure that the north express with all its wagons can continue on its way leaving behind the complete south train, with its wagons in the same order in which they appear in the drawing .

It is necessary to mention that in the lateral deviation (marked with the letter B) there is enough space for a car or locomotive only, as in the sections of the deviation marked with the letters A, C and D.

The problem is to say how many times the machinist of the North Express will have to change the direction of his locomotive to get this feat and what movements he must perform. Naturally, the damaged locomotive cannot be used as traction, but it can be dragged like any other car. All wagons can be moved individually or hooked together in the amount that is necessary.

The problem complies with the rules of ordinary practice and is offered to test your ingenuity and cunning by discovering the fastest way to get to the other side of the broken train.

#### Solution

The problem can be solved with 33 movements as indicated below:

We will identify the wagons and locomotives with letters from the nearest to the furthest: A, B, C, D, E, F, G, H, I so that the letter E would correspond to the damaged locomotive and the letter F would be the locomotive of the North express, it works.

First, locomotive F advances alone on track C until it is placed on track B and then goes back on track A until it is placed in front of locomotive E. These are two movements. Now, drag the locomotive E and place it on track D, release it and continue moving to the right to be able to go back and take the detour C to track B and then advance to track A, in total, 3 more movements that make a total of 5.

Now drag the wagon D to place it on track D and pushing the locomotive E to the right. Again, go back to the left to take the detour C to track B and proceed along track A to the left. There are 3 more movements that make a total of 8.

Repeat the same steps to place the car C on track D and move to the left of the turnoff (at the bottom). 3 more movements, 11 in total. Repeat the same movements to place car B on track D and turn left, 3 more movements, 14 in total. Finally, repeat the same steps taking the wagon A to track D and go back to the left, 3 more movements and 17 in total. Now all the wagons next to the broken locomotive are on the right and the machine on the left.

Now, the machine moves to the right, and takes the wagons A, B, C, D, the machine E and the wagon G to the left and goes back until leaving the wagon G at the turnoff B. 3 more movements, 20 total.

The machine takes the wagons A, B, C, D and the machine E to the left to be able to take the detour A and take them to the right crossing the D track, 2 more movements, 22 in total. Locomotive F moves only to the left on track D, returns back on track A until it engages carriage G and drives it to the left, 3 more movements, 25 in total.

Turn to the right by hooking all the wagons, including H and I. They are taken to the left and moved back to leave the wagons H and I at the turnoff (occupying sections A and B of the turnoff), 3 more movements, 28 in total.

Finally, drag G, A, B, C, D and E to the left to take the detour A and take all the wagons along with the broken locomotive to the right, 2 more movements, 30 in total.

Now the wagon G is carried to the left, it goes backwards by the detour A to hook the wagons H and I and it can resume its way normally, with the wagons in the same order of the beginning, this is 3 more movements that make a total of 33