“Nibiru” (& GENERAL) :- SOLVING 3x3
SLIDER-PUZZLES
Len Green 6th January 2006
lengreen@hotmail.com
FOREWORD
{A} Many Adventure players have serious troubles with slider puzzles, not
infrequently to the point of requesting save-games in order to by pass them.
The following is an attempt to remedy this, by illustrating that solving
a slider puzzle should not be a daunting prospect in any way!
{B} There is a very a suitable standard ‘square’ 3x3 slider puzzle in the
Quest/Adventure “Nibiru” which I shall use, merely as a typical example.
{C} With many sliders (but not all), a graphic picture is provided showing
the final objective. Generally this graphic is not available during the solving
process itself, and hence needs to be memorized, copied in some way, or
printed out. In at least one game however, the full final graphic is visible the
whole time … which naturally is a great help!
[[[ In the particular case of “Nibiru”, the final solution is also
available the whole time, but in a rather unusual way. The individual
final positions of the 8 tiles is revealed after ‘clearing’ the center
square, and then placing an amulet (from inventory) upon a button
there. This is described in the full “Nibiru” walkthroughs.
Alternatively, the Graphic #2 here can be memorized or
copied! ]]]
{D} If ANY slider puzzles are generated completely randomly, exactly
50% will be insoluble. In the case of “Nibiru” however, the Developers
have seen to it that every one of the huge number of randomly generated
sliders belongs to the 50% of puzzles which CAN ALWAYS be solved.
{E} A basically similar procedure to that described below can be used to
solve ALL standard (regular, square) slider-puzzles i.e. 4x4, 5x5, 6x6, etc.
However the larger they are, the more complicated they become (and hence
on the average will take longer to solve).
{F} ALL these ‘square’ sliders however, no matter how large or small,
have one thing in common! The bottom 2 rows are always the trickiest …
whilst those above are relatively easy to arrange.
In the case of the 3x3 slider as opposed to its larger brethren, there is
only one row above these bottom 2 rows (and it consists of only 3 tiles).
Hence the 3x3’s are particularly easy to solve!
But in ALL cases, the row or rows above these bottom 2 are
ALWAYS relatively easy to manipulate into the correct orientation(s) since
no attention whatsoever has to be paid to the bottom 2 rows whilst doing so!
Also, once the top row (or 2 rows, or 3 rows, or 4 rows, etc.) are
correctly placed THEY MUST NOT BE TOUCHED FOR THE
REMAINDER OF THE PUZZLE … ONLY THE BOTTOM 2 ROWS
HAVE TO BE MANEUVERED INTO THEIR CORRECT POSITIONS.
{G} All these puzzles are soluble using the same method. However, the
degree of complexity depends largely upon the initial randomly generated
configuration.
I have deliberately chosen a random start which is not the easiest I
have come across, but not the most difficult either. (This particular one can
be solved with 20 moves).
It’s worth mentioning that each of these puzzles can always be solved
in a number of different ways, some utilizing more or less slides than others.
{H} The general METHOD for solving these puzzles is the same for all
… and I shall attempt to explain it as best I can. However, it is very difficult
to do so without listing the moves for one particular individual randomly
generated example.
These are completely different for every one of the enormous number
of cases and hence are only an individual explanatory example and
CANNOT apply to anybody else’s actual case.
((( Hence ALL these unique moves/slides are displayed below in the following [
smaller, sea-green ] format. This is to differentiate them from general principles.
Hopefully, this will be clear !?! )))
(GENERAL) SOLUTION
Graphic #1
Graphic
#2
Graphic #1
This is a typical randomly generated “Nibiru” 3x3 slider puzzle …
just one of very many thousands I believe … and hence only used as an
example of the general procedure for solving.
The letters in red from A thro’ H at the top left corner of each tile
represent that actual tile itself (which can be slid once only each move, to an
adjacent EMPTY space, whenever/wherever that space is above, below, to
the right or to the left of the particular tile).
The numbers in black from 1 thro’ 9 at the bottom right corner of
each square represent each FIXED SQUARE itself.
Graphic #2
This is the final solution (… obviously for EVERY randomly
generated start configuration!).
PROCEDURE
Solving these puzzles (and by extrapolation, the larger conventional
square 4x4’s, 5x5’s, 6x6’s, etc.) can be expedited in 3 stages.
The 3rd stage should be trivial … and sometimes is not even
necessary, since by happenstance the final tiles sometimes are in place
‘automatically’ (an example of both these situations is outlined below)!
Stage-1 can be either easy or less so. The same applies to Stage-2. It
all depends upon the random initial distribution. Obviously if/when both
stages happen to be very easy, the slider-puzzle can be solved
EXTREMELY rapidly … and vice-versa if both stages are difficult!
But in the very worst case scenario, once you get the hang of the
SYSTEM, the solution for a 3x3 puzzle should take FAR less than 3
minutes.
STAGE-1
In the above typical example, you have to get tile C to its final position in
square 1, tile B ditto to square 2, and tile E ditto to square 3.
((( For this case ONLY, you must make the following ‘slides’ :In sequence, move (generally, left-mouse-click on) tiles which (temporarily)
reside upon the squares 4; 5; 2; 3; 6.
This just happens to be a particularly easy (random) performance, and produces the
situation shown in Graphic #3. )))
Graphic #3
Graphic
#4
Generally your start configuration will be far more bothersome than
the above random example. But do not worry, you will ALWAYS be able
to achieve this final correct top row … albeit frequently involving more than
the above 5 moves. The reason behind your guaranteed success in stage-1 is
due to the fact that you don’t pay any attention whatsoever throughout this
stage to what’s happening to the bottom 2 rows … and hence you have
complete flexibility.
WHEN YOU HAVE SUCCESFULLY COMPLETED STAGE-1,
DO NOT TOUCH ANY OF THE TILES IN THE TOP ROW
AGAIN DURING THE REMAINDER OF THE PUZZLE!!
STAGE-2
In this particular case, stage-2 happens to be more difficult and hence
entails more moves than the previous one … it all depends upon the random
initialization!
In this stage, you only deal with tiles in the bottom 2 rows (without of
course disturbing the previously fixed final top row).
You can perform this stage in somewhat different ways of which the
following is possibly the easiest.
In the specific case used as an example here, nearly all of the ‘work’
is simply to maneuver tile F into its final position in square 7, whilst
simultaneously moving tile G into its final position in square 4. You do
this without paying any attention whatsoever to any of the other tiles in the 2
bottom rows … and of course without touching any tiles in the top line!
( N.B. Alternatively any ADJACENT pair of tiles can be used in a
similar way … instead of the pair chosen above, i.e. F and G which were
chosen fairly arbitrarily as possibly being the ‘easiest’ to describe ).
There is a GENERAL foolproof method of doing this. View the tiles
in the bottom 2 rows CLOCKWISE starting from the bottom row right hand
corner … i.e. concentrate on the 6 squares clockwise from 9 thro’ 7 thro’ 4
thro’ 6.
All you have to do is to arrange these tiles so that (whether on the
middle or bottom rows) you get the F tile immediately before and touching
the G tile. After that. It’s child’s play!
((( In this case ONLY, one method is to make the following ‘slides’ :In sequence, move (generally, left-mouse-click on) tiles which (temporarily)
reside upon the squares 5; 8; 7; 4; 5; 6; 9; 8; 7; 4; 5; 8; 9; 6;
5; 4; 7; 8.
This is about 90% of the procedure. In this example, it produces the situation
shown in Graphic #4. )))
STAGE-3
Once stage-2 has been accomplished, all that remains is to rotate the
only remaining 3 tiles into their correct positions. This will often take only 3
moves … or at the most 6 moves.
If this cannot be done without touching ANYTHING ELSE, the
random generator has produced an insoluble puzzle!
((( In this specific case ONLY move (generally, left-mouse-click on) tiles which
(temporarily) reside upon the squares 9; 6; 5. )))
* * * * * * * * * * * * * * *
As mentioned previously, these puzzles can always be solved in a
number of different ways, some involving more or less slides than others.
Not infrequently, stage-3 is completely redundant.
Incidentally, in this particular example, I only included stage-3 at all
for the sake of ‘generality’ since it so happens that this one can be solved
without it. It can actually be completed with 6 slides less than the above and
without having to resort to stage-3 at all … not that this is of any
importance!
((( In this case (only of course), starting from Graphic #3, make the following
‘slides’ :In sequence, move (generally, left-mouse-click on) tiles which (temporarily)
reside upon the squares 5; 8; 9; 6; 5; 4; 7; 8; 5; 6. … See
Graphic #5. )))
Graphic #5
((( And finally, slide … 9; 8; 7; 4; 5.
This solves the above (individual) puzzle without having to use stage-3 at all. )))