SHUNTING PUZZLES THEORY |
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| 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? 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. 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 giving the correct answer (which is "man" - crawling in his infancy, walking in his prime and using a stick in old age) you would be killed by the terrible Sphinx... The origins of the word “puzzle“ 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. |
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Sequential movement puzzle + trains = "the shunting puzzle" |
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| 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's 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. |
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Model railway shunting puzzles - running a layout as a game |
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| Although it will probably never be
possible to determine where and when a railway modeller
had the idea to turn a model railway layout into a puzzle
for the first time, it is fair to assume that this didn't
happen out of mathematical interest but as a result of
trying to find a way to increase the fun to be had in
operating a model railway layout. Most certainly, it was
someone who liked playing games and solving puzzles. All model railway shunting puzzles seem to belong to one of two different general types: sequential movement (where a pre-determined order needs to be formed) and distributional ordering (where items must be placed where they belong). |
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Measuring complexity |
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| 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" the amount of cars which are selected 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?from this, 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). 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 |
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created: 24/FEB/2004 |
