deleted back to the drawing board... didnt think off patterns being found on same row in a house befor...
thanks red ed for the examples they help alot!
+-------+-------+-------+
| 7 . . | . . . | 1 4 . |
| . . . | . . 3 | . 6 8 |
| . . 2 | 8 . . | 5 . . |
+-------+-------+-------+
| 4 . 5 | . 1 . | . . . |
| . 2 . | . . . | . . . |
| . . . | 7 . 6 | . . . |
+-------+-------+-------+
| . . 6 | . . . | . 5 1 |
| . . . | 3 . . | 9 7 . |
| 2 . . | . . 9 | . . 4 |
+-------+-------+-------+
eleven wrote:... and only this one more, but i cant see a symmetry move.
Not very exciting ...
- Code: Select all
+-------+-------+-------+
| 7 . . | . . . | 1 4 . |
| . . . | . . 3 | . 6 8 |
| . . 2 | 8 . . | 5 . . |
+-------+-------+-------+
| 4 . 5 | . 1 . | . . . |
| . 2 . | . . . | . . . |
| . . . | 7 . 6 | . . . |
+-------+-------+-------+
| . . 6 | . . . | . 5 1 |
| . . . | 3 . . | 9 7 . |
| 2 . . | . . 9 | . . 4 |
+-------+-------+-------+
+-------------------+-------------------+-------------------+
| 7 5689 389 |*256 569 *25 | 1 4 23 |
| 159 459 149 | 1245 4579 3 | 27 6 8 |
| 13 46 2 | 8 467 147 | 5 9 37 |
+-------------------+-------------------+-------------------+
| 4 3 5 | 9 1 8 | 67 2 67 |
| 6 2 7 |*45 3 *45 | 8 1 9 |
| 89 1 89 | 7 2 6 | 4 3 5 |
+-------------------+-------------------+-------------------+
| 389 4789 6 |*24 478 *247 | 23 5 1 |
| 158 458 148 | 3 4568 1245 | 9 7 26 |
| 2 57 13 | 156 567 9 | 36 8 4 |
+-------------------+-------------------+-------------------+
+-------------------+-------------------+-------------------+
| 7 5689 389 |#256 569 25 | 1 4 *23 |
| 159 459 149 | 1245 4579 3 | 27 6 8 |
| 13 46 2 | 8 467 147 | 5 9 37 |
+-------------------+-------------------+-------------------+
| 4 3 5 | 9 1 8 | 67 2 67 |
| 6 2 7 |#45 3 45 | 8 1 9 |
| 89 1 89 | 7 2 6 | 4 3 5 |
+-------------------+-------------------+-------------------+
|-389 4789 6 |#24 478 247 |*23 5 1 |
| 158 458 148 | 3 4568 1245 | 9 7 26 |
| 2 57 *13 |#156 567 9 |-36 8 4 |
+-------------------+-------------------+-------------------+
eleven wrote:
- Code: Select all
M C N L S
1. Fixed boxes
R 8 107.495.424 3 N Mini-row symmetry
RC1 7 21.233.664 3 N
RC1C2 9 4.204.224 3 N
RC 10 2.508.084 3 N Mini-diagonal symmetry
M C N L S
1. Fixed boxes
C 8 107.495.424 3 N Mini-row symmetry
R1C 7 21.233.664 3 N MDS @ band 1, MRS @ band 2,3
R1R2C 9 4.204.224 3 N MDS @ band 1,2, MRS @ band 3
RC 10 2.508.084 3 N Mini-diagonal symmetry
udusuk wrote:r1579c4 from {12456} must have 1 or 2 or both
Stick Symmetry: r1c9+r7c7+r9c3 can't be [221]
=> r7c7+r9c3 can't be [21], must be [23|31|33] having 3
udusuk wrote:The next item on my wishlist is an example puzzle/solution grid for each of the 26 groups.
+-------+-------+-------+
| 1 7 6 | 2 5 4 | 3 9 8 |
| 3 9 4 | 1 7 8 | 2 5 6 |
| 2 8 5 | 3 6 9 | 1 4 7 |
+-------+-------+-------+
| 4 1 7 | 8 2 5 | 6 3 9 |
| 5 2 8 | 9 3 6 | 7 1 4 |
| 6 3 9 | 4 1 7 | 8 2 5 |
+-------+-------+-------+
| 9 4 1 | 7 8 2 | 5 6 3 |
| 7 6 3 | 5 4 1 | 9 8 2 |
| 8 5 2 | 6 9 3 | 4 7 1 |
+-------+-------+-------+
Sticks (1)(2)(3)(47)(58)(69)
S (123)(486)((597)
BxCxS (123)(456789)
+-------+-------+-------+
| 8 7 2 | 1 6 5 | 9 4 3 |
| 6 5 3 | 2 4 9 | 7 8 1 |
| 4 9 1 | 3 8 7 | 5 6 2 |
+-------+-------+-------+
| 7 2 4 | 9 1 6 | 8 3 5 |
| 5 3 8 | 7 2 4 | 6 1 9 |
| 9 1 6 | 5 3 8 | 4 2 7 |
+-------+-------+-------+
| 2 4 5 | 8 9 1 | 3 7 6 |
| 3 8 9 | 6 7 2 | 1 5 4 |
| 1 6 7 | 4 5 3 | 2 9 8 |
+-------+-------+-------+
Sticks (1)(2)(3)(47)(58)(69)
R (123)(486)(597)
BxCxR (123)(456789)
+-------+-------+-------+
| 6 9 1 | 4 7 2 | 8 5 3 |
| 5 4 3 | 9 8 1 | 7 6 2 |
| 2 8 7 | 3 6 5 | 1 4 9 |
+-------+-------+-------+
| 9 2 6 | 5 1 8 | 4 3 7 |
| 8 1 5 | 7 3 4 | 9 2 6 |
| 7 3 4 | 6 2 9 | 5 1 8 |
+-------+-------+-------+
| 1 6 9 | 2 4 7 | 3 8 5 |
| 3 7 8 | 1 5 6 | 2 9 4 |
| 4 5 2 | 8 9 3 | 6 7 1 |
+-------+-------+-------+
Sticks (1)(2)(3)(47)(58)(69)
SR2 (123)(486)(597)
BxCxSR2 (123)(456789)
I now have a catalogue of all of them (automorphic solution grids, that is) which I am in the process of canonicalising and deduping.udosuk wrote:The next item on my wishlist is an example puzzle/solution grid for each of the 26 groups.
1. Fixed boxes
R 8 : 123456789987123546645987132312564897879312465456879213231645978798231654564798321
RC1 7 : 123456789897123456645978123312564978978312564456897312581249637734681295269735841
RC1C2 9 : 123456789456789123789231645247395861691842537835617294374168952518924376962573418
RC 10 : 123456789456789123789123456214865937865937214937214865371542698542698371698371542
2. Boxes move in bands
S 25 : 123456789789123456645798123312564897897312564456879312231645978978231645564987231
SR1 28 : 123456789456789123789123456234891567591267834867534291348915672612378945975642318
SR1R2 30 : 123456789456789123789123456231897564567234891894561237315648972648972315972315648
SR 32 : 123456789897123654654879132312564978978312465546798321231645897789231546465987213
SC1 27 : 123456789456789123789123456234567891567891234891234567345678912678912345912345678
SR1C1 26 : 123456789456789123789231645231897456645123978897564231312978564564312897978645312
SR1R2C1 29 : 123456789456789123789231645231897456645123978897564231312645897564978312978312564
SRC1 31 : 123456789456789123789231645231564978645897231897123456312645897564978312978312564
3. Boxes move triangular (B 159, 267, 368)
BS 22 : 123456789456789123789123456235964817817235964964817235392641578578392641641578392
BSR1 24 : 123456789456789231789123645231564897564897312978312564312645978645978123897231456
BSR1C1 23 : 123456789457289163689173452235741896816392574974568231392817645568924317741635928
4. Rotational symmetries
DD2 79 : 123456789869127435457938126216374958785219643934685217671543892392861574548792361
DBxRx 86 : 123456789456789231789312456214938567375641892698527314561273948837194625942865173
5. Diagonal symmetries
D 37 : 123456789579128643684739125412673958958214376367985214831562497796841532245397861
DBS 43 : 123456789457189236968372514291738465374265198685941327546813972732694851819527643
DRC 40 : 123456789456789231789123645215348976398672514674915823541897362832564197967231458
6. Sticks symmetries
BxCx 134 : 123456789978213465546798231217864593835129674469375128752931846694582317381647952
BxCxR 135 : 123456789456789123789123456234591867567834291891267534378942615612375948945618372
BxCxS 145 : 123456789457189326689327154291635847745891632836742591318264975574918263962573418
BxCxSR2 144 : 123456789456789123789132465218967534564213978937548216391875642645321897872694351
BxCxSR 142 : 123456789456789123789123456214937865865214937937865214342678591591342678678591342
BxCxSR1R2 143 : 123456789456789123789132465248573916537961248961248537394815672672394851815627394
I counted 13. In fact all possible symmetries are built up very simple.udosuk wrote:(The 14 "classical" symmetries are actually of 8 essentially different ones as besides the 2 rotational symmetries all other 12 are actually 6 pairs, each in 2 orientations.)
A1 A2 A3 A1 C2 B3
B1 B2 B3 and B1 A2 C3
C1 C2 C3 C1 B2 A3
eleven wrote:In fact all possible symmetries are built up very simple.
We have the 2-cycled symmetries
- 180° rotational
- diagonal
- sticks, described here
the 4-cycled symmetry
- 90° rotational
and the 3-cycled symmetries.
ronk wrote:How would you correlate the above to gfroyle's Combinatorial Concepts With Sudoku I: Symmetry, Gordon Royle, March 29, 2006 ?
Additionally, discussion of this paper occurred at Sudoku Symmetry - Formalized.
eleven wrote:I counted 13.
udosuk wrote:the 2 links you cited are concerning the clue-pattern/shape symmetry of puzzles. In this thread Red Ed, eleven, I & others are talking about the automorphism symmetry of puzzles/solutions. Two different topics.
ronk wrote:How would you correlate the above to gfroyle's Combinatorial Concepts With Sudoku I: Symmetry, Gordon Royle, March 29, 2006 ?
udosuk wrote:Red Ed, I've just realised most of the example grids you listed are normalised. Which means I have my work cut out to work out the morphing operations to "expose" the symmetries. Very tough work!