Stormdoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby StrmCkr » Fri Dec 26, 2008 5:23 pm

Code: Select all
*--------------------------+--------------------------+---------------------------*
| ABC        .       .          | ABC        .       .          | ABC        .       .          |
|   .         DEF     .          |  .         DEF     .          |  .         DEF     .           |
|  .             .      GHJ     | .             .      GHJ       | .             .      GHJ        |
|--------------------------+--------------------------+---------------------------+
| ABC        .       .          | ABC        .       .          | ABC        .       .          |
|  .         DEF     .          |  .         DEF     .          |  .         DEF     .            |
|  .             .      GHJ     | .             .      GHJ       | .             .      GHJ        |
|--------------------------+--------------------------+---------------------------|
| ABC        .       .           | ABC        .       .          | ABC        .       .         |
|  .         DEF     .           |  .         DEF     .           |  .         DEF     .           |
|  .             .      GHJ      | .             .      GHJ        | .             .      GHJ       |
*--------------------------+--------------------------+---------------------------*


A typical
Stormduko puzzle
Is comprised of three concentric repeating patterns linked in unison, in such a way so that all-6 bands of a puzzle are equally distributed in 3 sets of 3 equal boxes. Also known as Automorphism.

All line of sights marked by a “.” To be equally distributing or replicating the pattern via reductions of line of sight.

Where as each Row and Column and Box shows the same pattern 3 times per area of presentations.

The grid would be represented as below.
Code: Select all
*---------------------------+-----------------------------+-----------------------------*
| ABC   GHI       DEF     | ABC   GHI       DEF      | ABC   GHI       DEF      |   
| GHI     DEF     ABC     | GHI     DEF     ABC      | GHI     DEF     ABC      |   
|  DEF   ABC     GHJ      | DEF    ABC     GHJ       |  DEF   ABC     GHJ       |
*---------------------------+-----------------------------+-----------------------------*
| ABC   GHI       DEF     | ABC   GHI       DEF      | ABC   GHI       DEF      |   
| GHI     DEF     ABC     | GHI     DEF     ABC      | GHI     DEF     ABC      |   
|  DEF   ABC     GHJ      | DEF    ABC     GHJ       |  DEF   ABC     GHJ       |
*---------------------------+-----------------------------+-----------------------------*
| ABC   GHI       DEF     | ABC   GHI       DEF      | ABC   GHI       DEF      |   
| GHI     DEF     ABC     | GHI     DEF     ABC      | GHI     DEF     ABC      |   
|  DEF   ABC     GHJ      | DEF    ABC     GHJ       |  DEF   ABC     GHJ       |
*---------------------------+-----------------------------+-----------------------------*


These grid loci’s are fixed integers and with the respect of permeations of rows or columns in a band can still change where that specific local is found.

Example of this.
Code: Select all
 column swap.
*---------------------------+
| GHI    ABC     DEF     |
| DEF    GHI     ABC     |
|  ABC   DEF    GHJ      |
*---------------------------+
(I am confident you can figure the others out)

How to apply the pattern?
First find a group of three digits.
That is linked via line of sight directly.

Code: Select all
 we three kings.
 *-----------*
 |5..|4..|8..|
 |..7|..5|..6|
 |...|.3.|...|
 |---+---+---|
 |7..|9..|4..|
 |...|..7|.9.|
 |..9|.2.|..8|
 |---+---+---|
 |64.|8..|.5.|
 |.25|..6|1..|
 |...|.1.|.24|
 *-----------*


Start with 4,9,8
Code: Select all
 *-----------*
 |.X.|4..|8..|
 |...|...|...|
 |...|...|...|
 |---+---+---|
 |.X.|9..|4..|
 |...|...|.9.|
 |..9|...|..8|
 |---+---+---|
 |.4.|8..|X..|
 |...|...|...|
 |...|...|..4|
 *-----------*


The implemented x’s mark where insertion of specific clues forms one of the three completed Stormduko patterns.


Pattern 1: 4,9,8
Code: Select all
 applied restrictions.
 *-----------*
 |.9.|4..|8..|
 |...|...|...|
 |...|...|...|
 |---+---+---|
 |.8.|9..|4..|
 |...|...|.9.|
 |..9|...|..8|
 |---+---+---|
 |.4.|8..|9..|
 |...|...|...|
 |...|...|..4|
 *-----------*

Note the rows and columns.

ABC = 4,8,9 @ R1C247, R4C247, R7C248,
Other candidates at – R5C8, R6C39, R9C4
{Form the completion conditions of the pattern. explained in a bit}

Pattern 2: 1,2,3
{These are found due to the conditions of line of sight}
Code: Select all
 *-----------*
 |...|...|...|
 |...|...|...|
 |x..|.3.|.x.|
 |---+---+---|
 |...|...|...|
 |...|...|...|
 |X..|.2.|.x.|
 |---+---+---|
 |...|...|...|
 |.2.|...|1..|
 |x..|.1.|.2.|
 *-----------*


Code: Select all
 apply pattern restrictions to fill it in.
 *-----------*
 |...|...|...|
 |...|...|...|
 |2..|.3.|.1.|
 |---+---+---|
 |...|...|...|
 |...|...|...|
 |1..|.2.|.3.|
 |---+---+---|
 |...|...|...|
 |.2.|...|1..|
 |3..|.1.|.2.|
 *-----------*


DEF: 1,2,3 @ R3C158, R6C158, R9C158
Other candidates at – R8C27

Pattern:3: 5,6,7
Code: Select all
*-----------*
 |5..|...|...|
 |..7|..5|..6|
 |...|...|...|
 |---+---+---|
 |7..|...|...|
 |..x|..7|..x|
 |...|...|...|
 |---+---+---|
 |...|...|.5.|
 |..5|..6|..x|
 |...|...|...|
 *-----------*

Code: Select all
 applied to fill in later
*-----------*
 |5..|...|...|
 |..7|..5|..6|
 |...|...|...|
 |---+---+---|
 |7..|...|...|
 |..6|..7|..5|
 |...|...|...|
 |---+---+---|
 |...|...|.5.|
 |..5|..6|..7|
 |...|...|...|
 *-----------*



GHJ: 5,6,7 @ R2C369, R5C689, R8C689
Other candidates at – R14C1,R7C8

Form the initial pattern based on the possible location of

ABC: @ R1C247, R4C247, R7C248
DEF: @ R3C158, R6C158, R9C158
GHJ: @ R2C369, R5C689, R8C689



Code: Select all
 which derives to form this arrangement. 
*----------------------+-------------------+----------------------*
|     .     ABC    .       | ABC   .       .      | ABC     .          .     |
|    .         .      GHJ   |    .        .     GHJ |   .          .       GHJ  |
|  DEF    .         .       |   .       DEF   .     |   .      DEF       .     |
*----------------------+-------------------+----------------------*
|     .     ABC    .       | ABC   .       .      | ABC     .          .     |
|    .         .      GHJ   |    .        .     GHJ |   .          .       GHJ  |
|  DEF    .         .       |   .       DEF   .     |   .      DEF       .     |
*----------------------+-------------------+----------------------*
|     .     ABC    .       | ABC   .       .      | ABC     .          .     |
|    .         .      GHJ   |    .        .     GHJ |   .          .       GHJ  |
|  DEF    .         .       |   .       DEF   .     |   .      DEF       .     |
*----------------------+-------------------+----------------------*


Extend it further to complete the grid.
Code: Select all
*--------------------------+---------------------------+-----------------------*
|GHJ     ABC    DEF     |GHJ     ABC    DEF     |ABC    GHJ    DEF |
|ABC    DEF    GHJ      |ABC    DEF    GHJ      |DEF     ABC   GHJ |   
|DEF    GHJ    ABC      |DEF    GHJ    ABC      |GHJ     DEF    ABC|
*--------------------------+---------------------------+-----------------------*
|GHJ     ABC    DEF     |GHJ     ABC    DEF     |ABC    GHJ    DEF |
|ABC    DEF    GHJ      |ABC    DEF    GHJ      |DEF     ABC   GHJ |   
|DEF    GHJ    ABC      |DEF    GHJ    ABC      |GHJ     DEF    ABC|
*--------------------------+---------------------------+-----------------------*
|GHJ     ABC    DEF     |GHJ     ABC    DEF     |ABC    GHJ    DEF |
|ABC    DEF    GHJ      |ABC    DEF    GHJ      |DEF     ABC   GHJ |   
|DEF    GHJ    ABC      |DEF    GHJ    ABC      |GHJ     DEF    ABC||
*--------------------------+---------------------------+-----------------------*


When the Stormduko aspect is present; all the remaining clues that are given will be found in their appropriate loci.

ABC: 4,9,8
DEF: 1,2,3
GHJ: 5,6,7

Check placement verse arrangement of pattern clues.

R14C1(57) = GHJ
R7C8(5) = GHJ
R8C27(12) = DEF
R5C8(5) = ABC
R6C39(89)= ABC
R9C9(4), = ABC

Since all aspects are true in all 9 boxes the Stormduko is true.


Apply line of sight limitations (which I have shown to each potential stormduko plot line)

Apply restrictions remove all other candidates not shown per cell.

Code: Select all
 *-----------*
 |59.|4..|8..|
 |..7|..5|..6|
 |2..|.3.|.1.|
 |---+---+---|
 |78.|9..|4..|
 |..6|..7|.95|
 |1.9|.2.|.38|
 |---+---+---|
 |64.|8..|95.|
 |.25|..6|1.7|
 |3..|.1.|.24|
 *-----------*

 
 *-----------------------------------------*
 | 5   9   13  | 4   67  12  | 8   7   23  |
 | 48  13  7   | 12  89  5   | 23  4   6   |
 | 2   6   48  | 67  3   89  | 57  1   9   |
 |-------------+-------------+-------------|
 | 7   8   23  | 9   56  13  | 4   6   12  |
 | 4   3   6   | 13  48  7   | 2   9   5   |
 | 1   5   9   | 56  2   4   | 67  3   8   |
 |-------------+-------------+-------------|
 | 6   4   1   | 8   7   23  | 9   5   3   |
 | 89  2   5   | 3   49  6   | 1   8   7   |
 | 3   7   8   | 57  1   9   | 6   2   4   |
 *-----------------------------------------*


The puzzle is now reduced to singles.

edit: i also forgot to mention the most important aspect.
3 sets of 3 boxs are equal directly.

{which would reduce the puzzle to singles further then i have shown.}

tecnically its all 9 boxs are equal to each other.
where as each box is a mirror/reflection or rotation of cells to each other based on line of sight. but its easist to see which is equal to the other directly based on appearance.

edit: fixed the names errors
Last edited by StrmCkr on Sun Dec 28, 2008 4:05 am, edited 2 times in total.
Some do, some teach, the rest look it up.
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StrmCkr
 
Posts: 624
Joined: 05 September 2006

Postby udosuk » Sun Dec 28, 2008 12:52 am

If I understand your concept correctly, in a "Stromduko" (or "Stormdoku" or whatever you like to call it) every mini-diagonal must contain one of 3 possible sets of 3 digits (in this puzzle {123},{489},{567}). If that's the case I don't understand why you showed so many steps above:

Code: Select all
+---+---+---+
|5..|4..|8..|
|..7|..5|..6|
|...|.3.|...|
+---+---+---+
|7..|9..|4..|
|...|.*7|.9.|
|..9|.2.|..8|
+---+---+---+
|64.|8..|.5.|
|.25|..6|1..|
|...|.1.|.24|
+---+---+---+

Only possible cell for 8 in b5 is in r5c5. Therefore r5c5=8.

All singles afterwards.:!:

Perhaps you should have given us a more difficult puzzle to demonstrate your "new techniques".:?:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby StrmCkr » Sun Dec 28, 2008 7:55 am

stormduko...:( typo i missed.

question: does it explain how to apply the stormduko property with some reason? rather then blind luck.


yes you are correct that every diagonal is constructed of sets of 3 digits.

and row,column and box.

all three can be used to form a cover set of digits. depending on how you wish to plot it, (diagonals+boxes), (columns rows) etc.

i showed many steps cause i figured it would be best if i did it that way to show what i mean.

its not a technique its a cover set application of pattern limitation.

Perhaps you should have given us a more difficult puzzle to demonstrate your "new techniques".


i'll have to construct a harder puzzle,:)


edit:
i have also found a way to make them a harder stormduko.

take the grids i showed
every box is actually equal initally/ only rearanged due to line of sight.

you could plot 1 box with x many fixed clues etc. (think its around 5 for min)

its up to the solver to figure out how the 9 boxes are orinatated to solve as 1 solution.
Some do, some teach, the rest look it up.
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StrmCkr
 
Posts: 624
Joined: 05 September 2006

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