


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: 14/MAR/2021
