Shunting Puzzle
There is a circular railway siding at the end of the main line.
C is a cattle truck,
S is a sheep truck,
E is an engine.
The engine can pass under the Foot Bridge but the two trucks cannot because they are too tall. The problem is to shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line.
This one was tricky!
Thomas, Mark, Lauran, Kay and Shoaib from the Tithe Barn Primary School worked hard on it. Sometimes it helps to work together. Their teacher says:
This was difficult, but totally absorbing. Working individually with pencil and paper little progress was being made. We started thinking as a group and decided to make a model of the problem. A red card was used to represent the cattle truck, a blue one for the sheep truck, a white one for the engine and an inverted 'V' shape piece of paper for the footbridge. A ruler was used for the main line and a circle drawn in pencil served as the railway siding.
On more than one occasion we thought we had solved the problem, but were unable to reproduce the result. The engine moves were recorded and after many attempts and much excitement we achieved it.
Here are the Shunting Instructions they came up with.
- From starting position reverse E from main line to siding LHS
- Change points. E forward to RHS to connect with S
- Reverse to LHS. Stop
- Change points. E forward pushing S into mainline
- Uncouple. E reverse to LHS and couple with C
- Change points. E pulls C to RHS and uncouple.
- E forward in anticlockwise direction - under the footbridge to LHS
- Change points. E forward into siding, The front of E couple with S
- Reverse to LHS
- Change points. E forward pushing S to connect with C on RHS.
- Reverse to LHS (E - S - C)
- Change points. Forward into mainline.
- Uncouple C
- Reverse E with S in front to LHS
- Change points. Disconnect S and leave on LHS
- Reverse E under footbridge in clockwise direction and round to LHS
- Change points. E only forward into mainline to couple with C
- Reverse to LHS. E pulls C
- Change points. E pushes C forward to RHS
- Uncouple C from E
- E reverses to LHS
- Change points. E forward into mainline
The trucks have changed places!
Josh (from Ampthill, Bedfordshire) also gave an excellent description of the solution:
The engine reverses on to the loop, then goes forward and connects to the sheep truck. It reverses and pulls this clockwise round the loop and then pushes it forward on to the main line. It reverses back on the loop then goes anti-clockwise round under the bridge and pushes the cattle truck on to the main line next to the sheep truck. Then it reverses and pulls both trucks back on the loop. Then it goes anti-clockwise and pushes the sheep truck back where it came from. Then it reverses pulling the cattle truck clockwise. Then it stops, goes forward and shunts the cattle truck on to the mainline. Then the engine reverses on its own back on to the loop, goes round clockwise under the bridge and carries on pushing the sheep truck round to where the cattle truck started off. Then the engine reverses and goes back on to the main line to get the cattle truck. It pulls the cattle truck back on to the loop, then changes direction and pushes it anti-clockwise to where the sheep truck was. Finally the engine reverses and then goes forward again on to the main line.
Well done!