Sliding Blocks puzzles have teased the minds of children and adults alike for more than 100 years. There is a peculiar fascination in pushing pieces of wood or plastic around a board to reach a particular position or achieve a certain objective. Once picked up and started, people find them hard to put down. Many sliding block puzzles are very easy to solve — designed presumably with children in mind. Some are extremely difficult to solve. However, the fascination does not stop at merely finding a solution. Especially with the easier type of puzzle, there is much greater satisfaction in finding the minimum move solution, or in the case of harder puzzles, a shorter solution than someone else’s.

 DEFINITION OF A SLIDING BLOCK PUZZLE

A sliding block puzzle consists of a group of pieces of any shape(s) enclosed within a confined area, in which the purpose is to rearrange the pieces either into a certain order or to get a particular piece to a specified position. This is accomplished by sliding the pieces or "blocks" —hence the name sliding block puzzles — usually one at a time into areas not occupied by other pieces. The lifting of pieces is never allowed — nor must they hop or jump over other pieces. They must be able to be moved by themselves i.e. there must be no requirement that they be pushed or pulled by other pieces as, for example, in railway shunting puzzles. Rotation of individual pieces (without lifting them) is only allowed if specifically stated. Pieces may be of any shape: square, rectangular, circular, triangular, L—shaped, etc.

Some puzzles contain obstacles or immovable barriers. Others introduce restrictions: for example pieces may have to follow specific routes (or lines) and may not be allowed to stop between points. There may be a requirement that certain pieces may never touch (orthogonally and/or diagonally) certain other pieces, for example, of the same colour; or that they do not “check” (as in chess) other pieces along the same line. In a few puzzles a piece (or pieces), sometimes of your choice, is not allowed to move at all.

DEFINITION OF A MOVE

There are three possible definitions of what constitutes a “move”: —

(i) Move one piece only in any one direction or combination of directions. (Under this definition a piece can move around a corner).

(ii) Move one piece only in any one direction.

(iii) Move any number of pieces together as a group in any one direction.

HISTORY AND DEVELOPMENT

No one seems to know when the first sliding block puzzle was invented or produced. What is certain is that Sam Lloyd made them famous one hundred years ago in the 1870’s with his still well known 14—15 puzzle. He did, however, take the idea for this puzzle, probably from an older French game/puzzle called Le Jeu de Taquain (see Recreations Mathematiques — by Edward Lucas). Henry Ernest Dudeney admitted in his book Amusements in Mathematics (1917) he took the idea of his puzzle — The Four Frogs from Guarini who produced a chess problem with four knights in 1512. But the movement of a knight, with its peculiar jump move, can hardly be described as a "sliding block" move.

After Sam Loyd’s 14—15 puzzle, many variations of this puzzle came onto the market, many with designs and pictures but all of them had pieces of uniform size. It was not until 1909 that a puzzle was patented that introduced rectangular pieces amongst square ones. There is no doubt that this puzzle is the one that has been most commercialised, appearing under literally hundreds of names. Barely a year goes by without some new version being produced. Puzzles in which rotation of the pieces was allowed were patented as early as 1906. It was the 1920’s and early l930’s that saw the explosion in sliding block puzzles and most of those that we have today are descended from this period. It was not long before non-convex (L—shaped) pieces were introduced into this type of puzzle and even puzzles with non-rectangular pieces were in circulation before 1924.

Double—sided puzzles (with one exception) are a comparatively modern development, limited, presumably because of the difficulty in linking the pieces together so that they do not fall out. The advent of plastics has now overcome this problem and in recent years many have appeared on the market.

Also modern are the 3—dimensional sliding block puzzles of which I know of only two.

 CLASSIFICATION OF TYPES

For ease of reference all sliding block puzzles have been classified into types as follows:—

CLASS A. Pattern arrangement puzzles
These are puzzles that have no set start position, it usually being required only to muddle up the pieces to “set” the puzzle.

CLASS B. Uniform piece puzzles
Puzzles in which all the pieces are of the same size and shape, usually square or circular.

CLASS C.  Rectangular piece puzzles
Puzzles in which there are square and rectangular pieces.

CLASS D.  Non-convex piece puzzles
The same as class C with the addition that one or more pieces will be non—convex, most usually L—shaped.

 CLASS E.  Restricted route puzzles
Puzzles in which pieces can only move along certain pre—determined lines.

 CLASS F.  Rotating niece puzzles
Puzzles in which rotation of the pieces is allowed.

CLASS G.  Special shaped piece puzzles
These may contain pieces of any shape e.g. triangular, etc.

CLASS H.  Double—sided and double layered puzzles
Puzzles containing either two layers of pieces or containing patterns or symbols on both sides of the pieces.

CLASS I.  Three—dimensional puzzles