SHUNTING PUZZLES

 
SHUNTING, as defined by the Oxford English Dictionary, primarily describes the act of "pushing or pulling a train or part of a train from the main line to a siding or from one line of rails to another: their train had been shunted into a siding".

While this conforms to British and Australian usage, its equivalent in North American railway terminology according to the US Department of Transportation is SWITCHING.

Evidently, the two terms denote the same and are completely interchangeable; the heading of this page, SHUNTING PUZZLES, can therefore also be read as SWITCHING PUZZLES.

My favourite definition of PUZZLE actually has a few layers of dust to it, as it comes from the 1911 edition of the Encyclopedia Britannica. However, as puzzles aren't new, it still captures the essence in a miraculously short sentence:

"PUZZLE: a perplexing question, particularly a mechanical toy or other device involving some constructional problem, to be solved by the exercise of patience or ingenuity."

 

 

Clearly, this is something real railways and railroads would like to keep to a minimum in daily operations. The two concepts are only brought together voluntarily in the field of railway modelling (model railroading) where shunting puzzles can generally be described as being reasonably compact layouts which - by way of definition through their name - have two basic characteristics:

 
1   First of all, they are concerned with shunting, meaning that they are conceived and built to allow rolling stock to be moved around on an appropriate track layout with sidings. On its own, this is simply the definition of a shunting layout.
     
2   Secondly, this shunting is not done according to spontaneous decisions of the operator but rather follows a framework of set rules which create a shunting order (usually by random selection of both the cars to be shunted and where they are to go), i.e. the operator is told what to do. This deliberately introduces a range of more or less complex and therefore difficult initial constellations of the rolling stock which is to be shunted, and thus creates the challenge of successfully tackling the given shunting order. It is this second aspect which is the key element in turning a shunting layout into a shunting puzzle.
 

A third characteristic, although arguably a matter of taste, is that shunting puzzles provide the most fun and sustained interest in operating per square inch of model railway layout ...

 
 



Shunting in progress in the sidings at Little Bazeley, a 00 scale UK shunting puzzle based on Inglenook Sidings

 

It will probably never be possible to determine where and when a railway modeller first had the idea to turn a shunting layout into a shunting puzzle. Most certainly, it was someone who was looking for ways to make operating the layout more fun, and probably also someone who liked playing games. The first example I know of is Alan Wright's way of operating his Wright Lines layout in the 1950s, ultimately leading up to his classic Inglenook Sidings, but there are bound to be earlier instances. The other "classic" switching puzzle is the Timesaver, devised by famed US modeller John Allen in the early 1970s.

The aim and purpose of this website is to illustrate and explain how different shunting puzzles work and how best to build and operate them. Over the years - not the least thanks to the rise of the internet - many variations and new types of model railway shunting puzzles have been conceived and successfully built and operated by a growing number of increasingly enthusiastic modellers. However, no matter if you are a complete newcomer to the subject or a seasoned shunting puzzler, it is always a good idea to look to the two classic shunting puzzles for information and inspiration.

All model railway shunting puzzles generally belong to one of two different types of puzzles: sequential movement (where a pre-determined order needs to be formed) and distributional ordering (where items must be placed where they belong).

 

DISTRIBUTIONAL ORDERING
SHUNTING PUZZLE

Solving a distributional ordering puzzle requires you to distribute individual elements of a puzzle in such a way that they end up being in what has been pre-determined as their correct place.

BEST KNOWN EXAMPLE:
JOHN ALLEN'S
TIMESAVER

The classic and by far the best known shunting puzzle: John Allen's Timesaver, which was originally presented in the November 1972 issue of Model Railroader.

 

SEQUENTIAL MOVEMENT
SHUNTING PUZZLE

Solving a sequential movement puzzle requires you to follow a series of sequential movements within a set of strict rules in order to arrive at a predetermined result.

BEST KNOWN EXAMPLE:
ALAN WRIGHT'S
INGLENOOK SIDINGS

The classic British shunting puzzle is Alan Wright's Inglenook Sidings, which originated in 1978 but dates back to a scheme already used by Alan Wright on his 1950s layout Wright Lines.

 
 

A LITTLE BIT OF
SHUNTING PUZZLE THEORY

 
Model railway shunting puzzles are fun because they give a sense to running trains by posing a challenge, and finding the solution to this challenge is both satisfying and entertaining. In this respect, shunting puzzles are like any other puzzle. Therefore, in order to take a "look behind the scene" and see how shunting puzzles work, it is best to start with the general question:
 

What exactly is a puzzle?

Puzzles come in many forms and styles, such as riddles, mazes, jigsaws, blocks, rings, wires, and lots more.

Some of the oldest "mechanical" puzzles come from China (perhaps the most familiar being the ch'i ch'iao t'u or Tangram), while the most well known historic European puzzle goes back to a tale from Ancient Greece, dating from 600 BC, and related by Sophocles and Apollodorus: The famous riddle of the Sphinx which sat on Mount Phikion and asked the Thebans "What has one voice, and is four-footed, two-footed and three-footed?" Unless travellers gavethe correct answer (which was "man" - crawling in his infancy, walking in his prime and using a stick in old age) they would be killed by the terrible Sphinx...

The origins of the word “puzzle“ itself are disputed. It has been suggested that the verb to puzzle, which appears at the end of the 16th century, is derived from the noun apposal (meaning "opposition"), indicating "a question for solution".

Others assume that the noun is in fact derived from the verb, which, in its earliest examples, means "to put in embarrassing material circumstances, to bewilder, to perplex". Some connection may also be found with a much earlier adjective poselet, meaning "confused, bewildered", which ceased to be used by the end of the 14th century.

 

 
 

Sequential movement puzzle + trains = "the shunting puzzle"

 
Jerry Slocum & Jack Botermans, who are the authors of a scientific study of the history and principles of puzzle games (Puzzles Old and New, University of Washington Press, 1992), provide an in-depth look at sequential movement puzzles.

Sequential movement puzzles are related to the well-known solitaire or peg puzzles, as well as the famous Rubick cube. The solution to this type of puzzle requires a user to follow a series of sequential movements within a set of strict rules in order to arrive at a predetermined result. Many puzzles of this type first appeared during the 18th and 19th century in Europe, often devised by mathematicians because they involve certain principles of topology, number theory, and combinatorics. However, as most of these puzzles are intended to be fun, they can actually be solved with a very basic mathematical knowledge - very often, logic and trial-and-error are quite sufficient.

One very famous such "mathematical puzzle" is in fact called the railway shunting puzzle.

 
There are a number of variations, but basically the problem which needs to be solved is that there are two trains facing each other on a single line with just one short siding (which won't hold one of the two equally long trains completely) available. In order to enable the two trains to pass each other and continue their journey, a string of sequential movements using the siding is required. It's quite a brain-teaser, which probably explains why railway companies all over the world took the more costly but easier way out and built passing sidings...  
 
 

Measuring complexity

 
A question which is often asked once the concept behind a shunting puzzle layout has been explained is as to the degree of complexity or, in other words: just how many possible configurations are there?

The mathematical approach to finding out how many permutations a specific shunting puzzle allows for is fairly easy. If "n" is the total number of cars on the shunting puzzle layout, and "k" is the amount of cars which are selected from this, then the formula to be used is

meaning that n factorial is divided through the factorial of n minus k (the “factorial” of three, for example, is 1 x 2 x 3 = 6, and written as "3!"). Applied to the original Inglenook formula (where 5 cars are selected froma total of 8), the calculation is as follows:

That is to say: the 8 cars can be arranged in 40,320 different ways on the Inglenook layout, and the number of possible trains with five cars which can be made up from these is 6,720.

In other words: if you were to systematically work your way through these combinations, solving four shunting tasks in one hour, and doing that for three hours every evening, you would be at it for 560 operating sessions totalling 28 hours.

The true beauty of a shunting puzzle is the simplicity within the complexity: both Inglenook Sidings and the Timesaver have simple rules, are easy to understand, straightforward to build, and great fun to operate and solve.

 
 

 

Page created: 23/SEP/2002
Last revised:27/MAR/2016