“Nibiru” (& GENERAL) :-  SOLVING  3x3  SLIDER-PUZZLES

Len Green     6th January 2006     [email protected]

 

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. )))