The only thing that I can see in the question to make me believe you are just looking at it in the wrong way is that you are basing your measurements by cutting everything in half. If we walked toward a wall with each step being half the distance of the next we would never reach it. But, however the trains are not taking half steps therefore they will indeed reach each other. Since they will reach each other I feel it would be safe to say that the minimum distance would be the width of one atom or there of. I know there are smaller things than atoms but I think you get the point. :-)