The New Sudoku Players' Forum

by **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

by **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". :?:

by **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.