About
BackSlide
by Christiaan Freeling
Obviously the history of BackSlide goes back to the invention of the '15' puzzle,
commonly attributed to Sam Loyd.
The set of 15 tiles used on both sides of
BackSlide is in fact a subset of a 16-tile set:
The tile with NO lines radiating from the center is missing in BackSlide
(for very obvious reasons). I defined the set in its complete
form , as one of a series of generalizations, in 1980, along with two ways to solve
it as a puzzle: trancendental andcompact .
Compact solutions are the ones provided in the SlideShow (with the blank filling
the hole).
Transcendental solutions are different in that they don't allow contact
between blank sides. Here's an example:
In both types of solution, the number of independent groups will always equal
the number of 'loops' in the figure (the blank counts as one group).
Another type of trancendental solution is called a 'StarMap'. In a StarMap, looking
along a line from any tile, one encounters - at some distance - a tile with a
matching line. Looking in a blank direction one encounters only nothingness.
The minimum size of a StarMap is 8x8. In this example, the 'blank' is
inside the constellation, and no two tiles are adjacent.
This is considered good form.
An Aknowledgement
Later I encountered this particular set in a different representation in a Dutch
book on games. I don't recall the inventor's name, but the year mentioned was 1975:
I obviously wasn't the first to discover it, though I made generalizations over
triangles, hexagons, cubes and rectangles, as well as 'second order sets', with lines
radiating towards corners also. The second order square set is called
'The Octopuszle' and has 256 elements. Finding a 16x16 compact solution can
be dangerous to your mental health.
The 15-puzzle
It was Thijs Krammer who first put the set in the 15-puzzle, thus making a
'one-sided BackSlide'. Later Ed van Zon wrote a program to solve the puzzle
in various ways. To eliminate rotations in the 15 variant, the 'four' was fixed
in the NW corner of the 2x2 center.
There appeared to be 81 class A solutions and 82 class
B solutions. A solution is always paired with its reflection
in the NW-SE axis. Only in the case of solution A1 in the pop-up menu is this
reflection identical to its original. Hence the odd number in class A.
Finally.
The idea of putting the same puzzle on the backside of the 15-variant came
naturally. The only question was how. Ed ran it through the computer and BackSlide
appeared to be the only mapping allowing meta-solutions other than the trival ones
(except of course the mapping with ONLY meta solutions).
BACKSLIDE ...
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