

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 predetermined 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 predetermined 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
possibly the best 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 fourfooted, twofooted and
threefooted?" 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 indepth look at sequential movement
puzzles. Sequential
movement puzzles are related to the wellknown 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 trialanderror 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 brainteaser, which
probably explains why railway companies all over
the world took the more costly but easier way out
and built passing sidings... 







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 (note that this calculation only
takes into account the rolling stock present on
the layout and disregards the distribution of the
three "empty slots" in the sidings, as
these are not part of the object of the puzzle
itself and only serve as manoeuvering space; if
you were to factor them in then the number of
combinations rises significantly).
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.




Further
reading




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. 





Page
created: 23/SEP/2002
Last revised: 26/DEC/2021
