A question often asked by both newcomers and veterans is whether or not there is a "best way" to tackle the Inglenook Sidings shunting puzzle. Well, there is at least a systematic way of looking at how to solve a specific Inglenook Sidings problem.
Rule of Thumb #1: "Get the whole picture"
In order to understand the systematics of the Inglenook Sidings shunting puzzle you need to take into account that there are 14 slots available where rolling stock can be placed at the end of a shunting move.

8 of these slots are occupied by rolling stock, leaving you with 6 free slots at all time. Try to focus not only on the freight stock (i.e. the occupied slots) - think of the free slots as items you can "move around" too. There is a moment in each randomly selected setup when having the free slots in the right places can be more important than where the freight stock actually is. Remember: the free slots define which piece of rolling stock can be moved where.

Rule of Thumb #2: "Clear the way"
Next, focus on the occupied slots which are not part of the setup you need to put together in order to solve the task you have been given (for the sake of clarity, the locomotive is always shown in the same position; when solving a real puzzle task, there is of course no need to move the locomotive to its starting point after each move).

You need to be able to move rolling stock around in order to successfully solve an Inglenook Sidings puzzle. In other words: it is important to get those cars out of the way which are in your way. The setup chosen to illustrate this principle makes this obvious: there isn't a single piece of rolling stock which you need to assemble into the order 1-2-3-4-5 which is accessible to begin with. So, you need to get the surplus cars (black) out of the way first before you can do anything else.

Other possible configurations may tempt you to start shuffling cars into the required order straight away, but unless you really have enough free slots to move around, all unwanted pieces of rolling stock should be moved to positions where they don't block moves.

Rule of Thumb #3: "Count backwards"
Once you can reach the required pieces of rolling stock, it is important to have a clear strategy. Placing car #3 in front of car #4 won't really help unless you can fit the other cars around this formation. It is generally easier to back up cars to the buffer stops than to build up the string of rolling stock from the loco end. In other words: count backwards, try to set off car #5 at the end of one spur and then add the appropriate cars to this. If that's not possible, try doing the same thing with car #4.

In our example setup, the positions of cars #5 and #4 need to be switched first.

With cars #4 and #5 in their correct sequence, attention now turns to the remaining three cars which, for the sake of illustration, have been placed in the most awkward positions - they're exactly the wrong way round, requiring the maximum moves to get them in the right order.

At this point, you need to remind yourself of rule of thumb #1 - make the empty slots part of your moves. In this case, this means coupling up to some of the rolling stock which is not part of the required configuration in order to gain room for shunting moves.

You can now back on to car #1, couple up, advance, back up to car #3, couple up, and your train is ready to depart with all cars in their correct order.

Now, that wasn't too difficult was it - how about another game...?


Further reading

  Blackburn Simon R. (2019) "Inglenook shunting puzzles", Electronic Journal of Combinatorics, Volume 26, Issue 2
Simon Blackburn is Professor of Pure Mathematics at the Department of Mathematics, Royal Holloway University of London. This article looks at the Inglenook Sidings from a mathematical perspective and answers the question when you can be sure this can always be done, while also addressing the problem of finding a solution in a minimum number of moves.

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Page created: 10/OCT/2006
Last revised: 09/JUNE/2019