The New Sudoku Players' Forum

[yzfwsf]

Hi experts, in order to add support for Gurth's Symmetrical Placement Theorem in the solver, we need to check whether the various morphs of the puzzle are adapted to Gurth's Symmetrical Placement Theorem to confirm. I know that there are 6^8=1679616 kinds of morphs, but obviously we don’t need to detect all of them. How can I find out which morphs need to be detected? Many thanks!
ps:I guess it may only need to detect 1/4 of them.

[ghfick]

I cannot be much help here but I am unsure how you are counting the morphs. 6 to the power 4 [6^4] is 1296. Wouldn't any morph have the same exclusions once you find the right symmetrical one?

[champagne]

Hi experts, in order to add support for Gurth's Symmetrical Placement Theorem in the solver, we need to check whether the various morphs of the puzzle are adapted to Gurth's Symmetrical Placement Theorem to confirm. I know that there are 6^8=1679616 kinds of morphs, but obviously we don’t need to detect all of them. How can I find out which morphs need to be detected? Many thanks!
ps:I guess it may only need to detect 1/4 of them.

I don't know what is the current status in my solver, but, I did the following :

My solver does not morph a puzzle, so, the puzzle must be shown in the right morph, recognized by the solver

Another process can morph any puzzle having a potential symmetry. Gsf had a better process. I know that because I submitted to the game several patterns with a limited symmetry and "gremlin" did not accept the pattern due to the fact that a better symmetry was possible.

IMO, applying the symmetry of given to a puzzle not in the right morph is nearly impossible to read.

[yzfwsf]

Thank you, I have confirmed that 6^8/4=419904 morphs need to be checked.

[StrmCkr]

http://forum.enjoysudoku.com/about-red-ed-s-sudoku-symmetry-group-t6526.html?hilit=gliding%20rows

technically no you don't need to do all the transformations

its specific in the above link there is a chart

1. Fixed boxes
Mini-Rows (MR) C 8 107.495.424 3 0 N equivalent to Mini-Columns (MC)
2 MR, 1 MD CR1 7 21.233.664 3 0 Y
1 MR, 2 MD CR1R2 9 4.204.224 3 0 Y
Mini-Diagonals(MD) CR 10 2.508.084 3 0 Y

2. Boxes move in bands
Jumping-Rows (JR) S 25 14.837.760 3 0 N
2 JR, 1 GR SR1 28 2.085.120 3 0 Y
1 JR, 2 GR SR1R2 30 294.912 3 0 Y
Gliding-Rows (GR) SR 32 6.342.480 3 0 Y
Full-Rows (FR) SC1 27 5.184 9 0 U
2 FR, 1 WR SR1C1 26 2.592 9 0 U
1 FR, 2 WR SR1R2C1 29 1.296 9 0 U
Waving-Rows (WR) SRC1 31 648 9 0 U

3. Boxes move triangular (B 159, 267, 368)
Jumping-Diagonals (JD) BS 22 323.928 3 0 Y also "Block symmetry"
Broken-Columns (BC) BSR1 24 288 9 0 U
Full-Diagonals(FD) BSR1C1 23 162 9 0 U

4. Rotational symmetries
Half-Turn (HT) DD2 79 155.492.352 2 1 Y also "180° rotational symmetry"
Quarter-Turn (QT) DBxRx 86 13.056 4 1 Y also "90° rotational symmetry", has HT symmetry too

5. Diagonal symmetries
Diagonal-Mirror (DM) D 37 30.258.432 2 9 Y also "diagonal symmetry"
DM+JD DBS 43 288 6 0 Y
DM+MD DRC 40 1.854 6 0 Y

6. Sticks symmetries
Column-Sticks (CS) BxCx 134 449.445.888 2 9 Y also "sticks symmetry"
CS+MC BxCxR 135 27.648 6 0 U
CS+JR BxCxS 145 13.824 6 0 U
CS+ GR/Band2,JR/B13 BxCxSR2 144 3.456 6 0 U
CS+GR BxCxSR 142 6.480 6 0 U
CS+ JR/B2,GR/B13 BxCxSR1R3 143 1.728 6 0 U

Meaning of the shortcuts of the equivalence operations (to be read from left to right, eg DBS means S after B after D)

B..cyclically move the bands downwards (B123->B231)
S..cyclically move the stacks rightwards (S123->S231)
Bx..exchange B1 and B3 (B123->B321)
Sx..exchange S1 and S3 (S123->S321)
R1 (R2, R3)..cyclically move the rows in band 1(2,3) downwards (r123->r231)
C1 (C2, C3)..cyclically move the columns in stack 1 (2.3) rightwards (c123->c231)
R..cyclically move the rows in all bands downwards (R1R2R3 or r123456789->r231564897)
C..cyclically move the colums in all stacks rightwards (C1C2C3 or r123456789->r231564897)
Rx..invert the order (exchange the first and 3rd) of the rows in all bands (r123456789->r321654987)
Cx..invert the order (exchange the first and 3rd) of the colums in all stacks (c123456789->c321654987)
D..mirror at the main diagonal from r1c1 to r9c9 (r123456789<->c123456789)
D2..mirror at the subdiagonal from r1c9 to r9c1 (r123456789<->c987654321)

all the valid move related transformations are marked "y"
these are the ones to focus on

for each of the types to verify the grid a maps to grid b you perform the transformation sequence as listed.
pay attention to what cells stay fixed:
cycling the grid transformations to have them all arrive in those locked spots. or manipulate the sequence so it locks the next set of rows/cols etc over 1.

the transformations needed to verify that the technique is valid on the grid only needs to cycle the other cells that aren't locked by the transformation into the spots that become locked.
which can be significantly less then all of them.

a bit more redacted but so far testing works with out having to manipulate al 3359232 transformations (6^8 * 2 )

if you are pursing the matter i suggest contacting Leren has a pretty good list of puzzles and what technique set they belong to for testing the engine out.

the only thing i will note is that if you are looking at each type individually some grids contain more then one type and can lead to extra transformations if programed individually.

[yzfwsf]

IMO, applying the symmetry of given to a puzzle not in the right morph is nearly impossible to read.

Maybe eleven can do.

[Leren]

yzfwsf wrote : Maybe eleven can do.

He sure can - see here.

BTW my gender type is XY, not XX.

Leren

[StrmCkr]

Sorry thought i removed that part to remain gender neutral
corrected