Single track
Problem
Two passenger trains with four carriages each are facing each other on the main line, with a siding branching off between them. The siding is only long enough to fit one engine and two carriages. What is the best way to shunt the carriages so that each train can continue its journey?
Student Solutions
This one needed a lot of patience, but Josh cracked it.
Train A reverses and allows Train B to pull forward.
Train B reverses up the siding and leaves carriages B3 and B 4 there.
Train B then pulls back on the main line and reverses.
Engine A then goes into the siding and reverses with carriages B3 and B4, taking them on the main line.
Engine B with carriage B1 and B2 then pulls forward far enough so it can reverse on to the siding.
Engine A then goes forward across the siding pushing carriages B3 and B4 in front and pulling A1, A2, A3 and A4 behind.
Engine B then pulls out of the siding with carriages B1 and B2 and goes forwards down the track.
Engine A then reverses, pushes carriages B3 and B4 into the siding, leaves them there, reverses back on the main rack and pulls forward.
Engine B then reverses into the siding with carriages B1 and B2 and picks up carriages B3 and B4.
Teachers' Resources
Why do this problem?
This problem is not for the faint hearted! It requires logical thinking and perseverance. Learners who enjoyed this problem may like to try Shunting Puzzle .Key questions
How could you start?
How will you remember what you have tried?
Remember that the engine can push and pull.
Perhaps using some counters will help?