The New Sudoku Players' Forum

by **gfroyle** » Fri Dec 02, 2005 8:50 am

Here are some nice symmetric 18s... numbers 5, 6 and 8 seem to be hardish, but the others are OK.

http://www.csse.uwa.edu.au/~gordon/sudokupat.php?cn=8

Enjoy!

Gordon

by **olimpia** » Sun Mar 15, 2009 7:56 am

Those are cool. I like them

I know you posted this a long time ago, so maybe your aren't looking for replies anymore. But one very minor suggestion is that I wish the blank cells were represented with something besides a "+". (like a period or just a space) The symmetry gets visually lost a little bit when the clues are mixed in with + symbols.

It looks like the sudokus you posted concentrate on rotational symmetry. Some 18s with reflection symmetry can also be found here (18s with reflection on one axis, and 19s with two axis):

http://www.flickr.com/photos/npcomplete/

by **m_b_metcalf** » Mon Mar 16, 2009 11:34 pm

olimpia wrote:Those are cool. I like them

Olimpia,

These beasts have also been observed lurking here and here.

Regards,

Mike Metcalf

by **olimpia** » Fri May 15, 2009 2:08 am

Here's another with reflection symmetry:

"18 clue reflection / shape #26"

Code: Select all: . 5 . . . . . 9 . . 3 . . . . . 6 . . . 4 7 . 8 2 . . . . 2 . 3 . 4 . . . . 7 . . . 1 . . . . . . 5 . . . . . . . 2 . 4 . . . . 9 . . . . . 3 . . . . . . . . . .

I have been collecting 18 clue sudokus with reflection symmetry and I think this is a new shape. Its the 26th shape in my journal.

For a discussion about the frequency (or scarcity) of these sudokus check here:

http://forum.enjoysudoku.com/viewtopic.php?t=6709&highlight=

by **olimpia** » Thu Jul 29, 2010 12:07 am

Thanks to the members who restored the players forum!

Some of the discussion about these 18s was lost, but I did keep a record of all 18s with horizontal symmetry. A total of 97 have been discovered, and some people speculated that this may be near the total that exist. In any case I kept a record of them (from the previous forum the new forum or the rico.alan website).

Here they are:

Code: Select all: 1. mauricio 2. mauricio 3. mauricio 4. mauricio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . 1 . 2 . . . . . . 1 . 2 . . . . . 1 . 2 . 3 . . . . 2 3 . 4 5 . . . . 3 . . . 4 . . . . 3 . . . 4 . . . . . . . . . . . . . . 2 . 6 . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . 5 . . 4 . . . . . 7 . . . 4 . . . 5 . . . . 4 . . . 5 . . . 5 . 4 . 6 . 7 . . 8 . . . . . 1 . . 1 . 6 . 7 . 2 . . 1 . 6 . 7 . 2 . . . 3 . . . 2 . . . . 3 . . . 6 . . . . . . 5 . . . . . . . . 5 . . . . . . 8 . . . 1 . . . . 5 . . . 2 . . . 2 . . . . . 6 . 2 . . . . . . . 6 . 7 . 5 . 9 . 4 . . 1 . . 8 . . 4 . 7 8 . . 4 . . 1 2 8 7 . . 4 . . 1 2 5. mauricio 6. mauricio 7. mauricio 8. olimpia . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . . . . . 9 . . . . 1 . 2 . . . . . . 1 . 2 . . . . . . 1 . 2 . . . . 3 . . . . . 6 . . . 3 . . . 4 . . . . 3 . . . 4 . . . . 3 . . . 4 . . . . 4 7 . 8 2 . . . . . . . . . . . . . . . . . . . . . . . . 5 . . . . . . 2 . 3 . 4 . . . . 4 . 3 . 5 . . . 1 . 5 . 6 . 2 . . 6 . . . . . 7 . . . 7 . . . 1 . . . 1 . 6 . 7 . 2 . 2 . 4 . . . 7 . 1 . 7 . . . . . 8 . . . . . 5 . . . . . . . 8 5 4 . . . . . . . 3 . . . . . . 1 . . . 3 . . . . . 2 . 4 . . . . 2 . . . . . 1 . . . 8 . 4 . 6 . . . . 4 . 3 . 5 . . . 9 . . . . . 3 . . 9 . . . . . 6 . . 5 . . . . . 1 . . 2 . 8 . 7 . 9 . . . . . . . . . . 9. Rico Alan,R828-S11 10. olimpia 11. mauricio,heart 12. Vic Reinhart,Raphael . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . 3 . . . . . 1 . 3 . 5 . . . . . 1 . 2 . . . . 9 . . 1 . . 3 . 8 . . . 1 . . . 9 . . . 2 . 4 . . . . . 1 . 3 . 4 . . . . 6 . 2 . 7 . . . 3 2 . . . 5 6 . . 2 . . . . . 8 . . . 4 . . . 1 . . . . . 3 . 4 . . . . . 6 . . . 3 . . . . 3 . 9 . 1 . . . . 5 . . . 3 . . 2 1 . . . . . 9 8 . . . . 4 . . . . . . . . 5 . . . . . 2 . 6 . 7 . 8 . . . . . . . . . . . . . 6 . 5 . . . . 4 . 6 . 8 . 2 . . . . . 5 . . . . . . 2 5 . 6 4 . . 9 1 . . . . . 7 4 . . 5 . 7 . 9 . . . 7 . . . . . 6 . . 8 . . . . . 1 . . . . . . . . . . . . . . . . . . . . 8 . . . . . 2 . . . . . . . . . . 13. Vic Reinhart,Odyssey 14. Vic Reinhart,Electra 15. mauricio 16. Rico Alan,R828-S09 . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . 7 . . 1 . . 6 . . 5 . . . . . 7 . . . . 1 . 2 . . . 1 2 . . . . . 8 4 . . 9 . . . 2 . . . . 7 2 . 3 6 . . . 3 4 . . . 5 6 . . 3 . . . . . 7 . . . . 2 . 3 . . . . . . . . . . . . . . . . 3 . . . . . . 4 . . . 6 . . 5 6 . . . . . 1 8 8 1 . . . . . 9 5 1 . . . . . . . 7 . . . 2 . 3 . . . . . . . . . . . . . . . 4 . 2 . . . 7 . . . . . . . 8 . . 5 . . . 9 . . . . 3 4 . 2 9 . . . . 3 . . . 2 . . . . . 7 . 8 . . . . . 6 . 9 . 5 . . . 1 . . 5 . . 8 . . 9 . . 5 . . 1 . . 2 . . . . . 4 . . 7 . . . . . 2 . . . . . . . . . . . . . . . . . . . . 6 . . 5 . . 3 . . . . . 5 . . . . 17. Vic Reinhart,El Morro 18. tarek 19. olimpia 20. mauricio . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . . 2 . . 7 . . . 8 . . . 3 . . . 3 . . 1 . . 2 . . . 1 . . . 2 . . . . 8 . . . 4 . . . 4 . 2 . 7 . 6 . . . 6 . . . 5 . . . 3 . . 4 . . 5 . . . . 3 . 4 . . . . . . . . . . . . . 8 . . 2 . . 4 . . . . . 3 . . . . . 1 . . . . . 9 . . 7 . . . . . 4 . . . 5 . . . 8 . . . . 2 . . . 6 . . . . . . 7 . . . . . . 3 . 1 . 8 . . . . . . 3 . . . . . . 7 . . . 1 . . . . 4 5 . 6 3 . . . 2 . 6 . 4 . 7 . . . 8 5 . 6 9 . . . . . 1 . 6 . . . . 2 . . 9 . . 1 . . . 5 . 3 . 1 . . . 2 . . 4 . . 1 . . 5 . . . . . 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . 4 . 7 . 3 . 21. Rico Alan,R828-S12 22. mauricio 23. Rico Alan,R828-S10 24. Vic Reinhart,Lulin . . . . 8 . . . . . . . . . . . . . 1 . 2 . . . 5 . 3 8 6 . . . . . 1 4 2 1 . . . . . 3 4 . . 1 . . . 2 . . . . . . 8 . . . . 5 . . . . . . . 6 3 . . . . . . . 2 . 3 . . 4 . . 5 . 3 . . . . . . . 4 . . . . 1 . . . . . 6 . . . . . 5 . . . . . 3 . . . . . . 9 . . . 2 . . . . . 8 . 2 . . . . . 8 . . . 9 . . . . 6 . . . 7 . . . . . 3 . 5 . . . . . 7 . . . 3 . . . . . 3 . 7 . . . 2 . 8 . . . 1 . 6 . 8 . . . . . 6 . . . . 6 . 4 . . . . . 5 . . . 6 . . . . . 1 . 8 . . . . . . . . . . . . . . 1 . 5 . 9 . . . . . . . . . . . . 4 . . . . . 8 . . 6 . . 9 . . 2 . . . . . . . . . . 7 . . . 9 . . . 3 . 5 . . . . . 2 . 5 . . . . . . . 1 4 . . . . . . . 8 25. olimpia 26. olimpia 27. olimpia 28. mauricio . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . 2 . . . 3 . 3 . . 1 . . 4 . . 6 . . . . . 5 . 5 . . . 2 . . . 4 . 4 . . . . . 5 . . . 7 . . . 5 . . . . 7 . 1 . 2 . . . 6 . . . . . 5 . . . . . . . . . . . . . . 2 . . . . . . . . 2 . . . . . . 7 . . . 2 . . . . . 6 . 4 . . . . . 5 . . . 6 . . . 7 . . . . . 6 . . 8 . 5 . 6 . 7 . 3 . . . . . . . 1 . 4 . . 3 . . 2 . . . 1 . 3 . 4 . . . . . . 3 . . . . 2 . . . . . . . 7 . . . . 4 . . . . . . . . 4 . . . . . . 2 . 4 . 3 . . . . . . 3 . . . . . . 8 5 . 6 9 . . . 8 . 5 . 6 . 9 . . 1 . . . . . 6 . . 8 . . . . . 6 . . 1 . . . . . 3 . 2 . . . . . . . 8 . . . . . . . . . . 5 . 8 . 9 . 4 . 29. mauricio 30. mauricio 31. mauricio 32. mauricio 1 . . . 2 . . . 3 1 . . . 2 . . . 3 . . . . 1 . . . . 1 . . . 2 . . . 3 . 4 . . . . . 5 . . 4 . 5 . 6 . 7 . . . . . 2 . . . . . 4 . . . . . 5 . . . . . . . . . . . . . . . . . . . . . 3 . . . 4 . . . . . . 1 . . . . . . . 6 . 4 . . . . . . 8 . 4 . . . . . . . 5 . . . . . . . 6 . 7 . . . 2 . . . . . . . 7 . . . . 3 . . . . . . 4 3 . 6 7 . . 3 . . . . . . . 1 . . 3 . . . 8 . . 9 . . . . . . . 1 . 1 . . . . . 8 . 8 . . . . . . . 2 . . . 2 . 5 . . . . . . . 9 . . . . . . . 4 . 7 . . . . 7 . . . . . 4 . . 5 . . 7 . . 9 . . 5 . . . . . 4 . . 2 . . 8 . . 1 . . . . . . . . . . . 6 . . . . . 4 . . 8 . . 1 . . 5 . . 8 . . . . . 3 . . 6 . 4 . 9 . 7 . 33. mauricio 34. mauricio 35. mauricio 36. mauricio . . . . . . . . . 1 . . . . . . . 2 1 . . . . . . . 2 . . . . . . . . . . . 1 . . . 2 . . . 3 . 4 . 5 . 6 . . 3 . 4 . 5 . 6 . . . 1 . . . 2 . . . . 2 3 . 4 5 . . . . . . . . . . . . . . . . . . . . . 3 . 4 . 5 . 6 . . . . . 6 . . . . . . . 7 . 3 . . . . . . 7 . 6 . . . . . . . 1 . . . . . . 3 . . . 1 . . 2 . . . . . . . 5 . . 2 . . . 5 . . . 7 . . . . . 3 . . 6 . . 7 . . 8 . 8 . . . . . . . 1 8 . . . . . . . 1 3 6 . . . . . 4 8 . . . 5 . 2 . . . . . . . 8 . . . . . . . . 8 . . . . . . . . 7 . . . . . 8 . . . . . 7 . . 6 . . . . . 3 . . 6 . . . . . 3 . . . . 3 . 6 . . . 9 . . . . . . . 6 . 7 . . 1 . . 4 . . 7 . . 1 . . 4 . . . 2 . . . 9 . . 37. mauricio 38. mauricio 39. mauricio 40. mauricio . . . . . . . . . . . . . 1 . . . . 1 . . . 2 . . . 3 1 . . . 2 . . . 3 . . 1 . . . 2 . . . . 1 . . . 2 . . . 4 . 5 . 6 . 7 . . 4 . . . . . 5 . . 3 . 4 . 5 . 6 . . . 2 . . . 3 . . . . . . . . . . . . . . 3 . 6 . . . . . . . 1 . . . . . . . 2 . 3 . . . . . . 8 . 7 . . . . . . 7 . 5 . . . . 4 . . . . . 3 . . . . 4 . 5 . . . 3 . . . . . . . 2 2 . . . . . . . 1 6 . . . . . . . 4 . 6 . . . . . 7 . 6 . . . . . . . 1 3 . . . . . . . 6 . . . 3 . 7 . . . . . 3 . . . 5 . . . . . . 6 . . . . . . . . 1 . . . . . . 2 . . . 1 . . . 7 . . 8 . . 1 . . 8 . . . . . 4 . . 8 . . . . . 4 . . . 8 . 9 . 7 . . . 8 . . . . . 6 . . 7 . . . . . 5 . . 5 . . . . . 7 . 41. mauricio 42. mauricio 43. olimpia 44. mauricio 1 . 2 . . . 3 . 4 1 . 2 . . . 3 . 4 . . . . 1 . . . . . . . . . . . . . . 5 . 6 . 7 . 8 . . 5 . 6 . 7 . 8 . . 4 . . 2 . . 3 . . . 1 . 2 . 3 . . . . . . . . . . . . . . . . . . . . . . 7 . . . 5 . . . 4 . 1 . 5 . 6 . . . . 5 . 8 . . . . . . 5 . 8 . . . . . . . 3 . . . . . . . . 7 . . . . 3 . . . . . . . 7 3 . . . . . . . 2 . 3 . . 4 . . 2 . . 6 . . . . . 4 . 4 . . . . . . . 1 . . 8 . . . 1 . . . . 6 . . . 8 . . . 8 . . . . . 5 . . . . . 3 . . . . . . . . 3 . . . . . . . 5 . 6 . . . . . . 4 . 8 . . . . 6 . . . . . 5 . . 6 . . . . . 5 . . . 8 . . . 6 . . . . 7 . . . 2 . . . . . . 1 . . . . . . . . 1 . . . . . 1 . . . . . 4 . 3 . . . . . . . 1 45. Vic Reinhart,Oaxaca 46. mauricio,spaceship 47. Rico Alan,R747-S13 48. Rico Alan,Jade . . . 4 . 5 . . . . . . . 1 . . . . . . . . 8 . . . . 8 1 . . . . . 4 9 2 . . . . . . . 1 . . 2 . . . 3 . . 1 3 . . . . . 5 7 2 . . . . . . . 1 . 3 . . . . . 7 . . 4 . . . . . 5 . . 2 . . . . . 3 . . . . 5 . 7 . . . . . 6 . . . 5 . . . . . 1 6 7 . . . . . 4 . 6 . 9 . . . . 2 . 8 . 7 . . . . . 2 . 3 . . . . . 3 . . . 4 . . . . . . . . . . . . . 5 . . . 6 . . . . . . 1 . . . . . . 8 . . . 5 . . . . . 3 . 7 . . . . . . . 9 . . . . . . . . 2 . . . . . . . 4 . 3 . . . . . 8 . 4 . 6 . . . . . 6 . 3 . . . . . 5 . . . 6 . . 6 . . . . . . . 1 . 5 . . . . . 7 . . . . . . . . . . . 1 4 . . . 7 9 . 9 . . . . . . . 7 . . . . 9 . . . . 1 . . . . . . . 8 49. olimpia 50. olimpia 51. olimpia 52. olimpia . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . 2 . 3 . . . . 3 . . 1 . . 2 . 4 . . . 2 . . . 8 8 4 . . . . . 3 2 7 . . . 1 . . . 4 . . 6 . . . 5 . . 8 3 . . . . . 4 7 . 3 . . . . . 8 . 6 . . . . . . . 5 7 . . . . . . . 5 . . 9 . . . 6 . . . . 1 . . . 2 . . 5 . . . . . . . 6 . 1 . . 2 . . 4 . . . . 3 . 4 . . . . . . 3 . 4 . . . . . . . . . . . . . . . . 3 . . . . . . . . 5 . . . . . . 5 . . . 3 . . . 7 . . 2 . . 9 . . . 8 5 . 6 7 . . . . 1 . 6 . 9 . . . . 6 . . . 5 . . . 2 . . . . . 8 . . 2 . . 4 . . 1 . . 8 . . . . . 3 . . 7 . . . . . 4 . . 9 . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . 5 . 4 . . . 53. olimpia 54. olimpia 55. Ano1 56. Ano1 . . . . 1 . . . . . . . . 1 . . . . . . . 7 . 3 . . . . . . . . . . . . 5 . . . . . . . 3 1 . . . . . . . 9 . 1 . . . . . 2 . . . . 1 . 5 . . . 4 3 . . . . . 6 5 2 . . . . . . . 3 . . . 5 . 9 . . . . . 7 . . . 3 . . . . 7 . . . 1 . . 3 . . . . . . . 7 . . 5 . . . 9 . . . 9 . . 3 . . 1 . . 5 . 3 . 4 . 8 . . 7 . . 6 . . 5 . . 6 . . 4 . . 1 . . . 4 . 2 . 7 . . . . . . . . . . . . 8 . 5 . 2 . 6 . . . 3 . . . 6 . . . 5 . . 6 . . 8 . . . 2 . . . 9 . . . 6 . . . . . 7 . . . . . 6 . . . . . . 6 . 7 . 2 . . . 6 . . . . . 5 . . . . 4 . 3 . . . 9 . 7 . . . 5 . 4 . 1 . . . . . 9 . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57. Ano1 58. Ano1 59. Ano1 60. Ano1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . 6 . . . . . 4 . . . 6 . . . . 1 . . . 9 . . . . 6 . . . 7 . . . . 5 . . . 4 . . . . . 2 7 5 . . . . 4 . 2 . 7 . 8 . . . . 1 . 3 . . . . . . 4 . 8 . . . . . 6 . . . 1 . . . . . . 9 . . . . . . 4 . 6 . 2 . . . . 9 . 1 . 2 . . . 3 . . 5 . . 9 . . . . 8 . 4 . . . . . . 9 . 8 . . . . . . . . . . . . . . 9 . . . 4 . . . . 5 . . . 1 . . . . 8 . . . 3 . . . . 7 . . . 8 . . . . . 6 . 1 . . . 8 7 . . . . . 4 6 . 2 . . . . . 1 . . 4 . . . . . 3 . . 2 . . . . . 3 . 4 . . . . . . . 2 1 . . . . . . . 9 8 . . . . . . . 6 . 5 . . . . . 7 . . . . . 5 . . . . 7 . . . 4 . . . 8 . 6 . . 3 . . 7 . 61. Ano1 62. Ano1 63. Ano1 64. Ano1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . 3 . . . . . . 4 . 2 . . . . . 8 . . . 3 . . . . 6 . 4 . 3 . . . . 5 . 7 . 2 . . . . 6 . 7 . 3 . . . 9 . 1 . 2 . 6 . . 2 . . . . . 7 . . 9 . . . . . 6 . . . . . . . . . . 1 . . . 3 . . . 6 9 7 . . . . . 5 1 . . 4 . 2 . 1 . . . . 1 . 6 . 7 . . 2 6 . . . . . 7 9 . 1 . . . . . 9 . . 3 . . . . . 8 . . 9 . . . . . 4 . . . . . 8 . . . . . . . . 8 . . . . 7 . 2 . . . 5 . 4 7 . 8 . . . 6 . 3 . . . 8 . 6 . . . . . . 5 . 1 . . . . . . 3 . 8 . . . . 4 . 2 . 9 . 5 . . . 7 . . . 4 . . 4 . 3 . . . 8 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65. Ano1 66. Ano1 67. Ano1 68. Ano1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . 9 . . . 6 . 4 . . . 2 . 1 . . . . 9 . 6 7 1 . 2 . . . 7 . 3 . 5 . . . . . 5 . 1 . . . . . 7 . . . 8 . . . . 8 . . . 4 . . . 8 . . 7 . . 2 . . . . . 8 . . . . . 6 . . . . . 5 . . . . 8 4 5 . . . 9 . 3 . . . 7 . 1 . 5 . . . . . 7 . . . 5 . 7 . 3 . . . . . . 2 . . . . . 6 . 4 . 2 . 8 . . . 2 3 9 4 8 . . . . . 4 . 8 . . . . 1 . . . . . 6 . . . . . . . . . . . 7 . . . . . 3 . . . . . 8 . . . . . . 4 . 3 . 8 . . . . . 2 . 8 . . . 4 . . . . . . . 9 . 1 . . . . . 9 . . 6 . . . . . 7 . . . 9 . . . 3 . . . . . . . . . . . 8 2 . . . . . 6 1 . . . . . . . . . . . . . . . . . . 69. Ano1 70. Ano1 71. Ano1 72. Ano1 . . . . 5 . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 8 . . . . . 3 . 8 . 9 . . . 2 . . 3 . . 9 . . . . 9 5 4 . . . . . . . . . . . . . 5 . . . . . 7 . . . 7 . 8 . 6 . . . 6 . . . . . 7 . . 3 . . . . . 7 . . . 2 . . . 6 . . . . . . 7 . . . . . . . . . . . . . 4 . . . 9 . . . 1 . . . 3 . 1 . . . . . 1 . 6 . 3 . . . 2 . 6 . 8 . 9 . . . . . 5 . . . . . . 9 . . . 8 . . . 9 . . . . . 2 . . . 3 . 4 . 5 . . 1 . 8 . . . 6 . 4 . . . 8 9 6 . . . . . 6 . . . 8 . . . . . 7 . 2 . . . . 5 . . 7 . . 3 . . . . . 4 . . . . . 4 . 5 . 2 . 1 . 5 . 4 . . . 3 . 1 8 . . . . . . . 6 . 1 . . . . . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73. Ano1 74. Ano1 75. Ano1 76. Ano1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . 7 . . 4 . 9 . 3 . 8 . . . 6 . . . 1 . . . . 1 . . . 5 . . . . . 4 . 8 . . . . . 5 . . . 6 . . . 4 . . . . . 2 . . 6 . 8 . 4 . 2 . . . 4 . 9 . 1 . . . 8 . . . . . 5 . . . 3 2 1 6 7 . . 9 4 . . . . . 8 2 . . . . 5 . . . . . . 2 . 6 . 7 . . . 9 . . . . . 4 . 8 . . . . . . . 6 8 . 1 . 3 . 4 . 6 . . . 1 . 2 . . . . . . . 7 . . . . . . . . 7 . . . . . 5 . . 7 . . 3 . . . 6 . 5 . 1 . . . . . 9 . 5 . . . . . . 2 . 6 . . . . . 8 . . . 6 . . . 9 . . . . . 3 . 1 . 7 . . . 6 . 3 . . 5 . 1 . 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77. Ano1 78. Ano1 79. Ano1 80. Ano1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . 6 . . . 8 . 7 . 6 . . . 1 . . . . . 2 . . . 2 . 4 . 6 . . . . 4 . . . 3 . . . . . 3 . 4 . . . . . . 6 7 8 . . . . 8 . . . . . 1 . . . . 5 . 7 . . . . . 2 . . . 7 . . . 2 . . . . . 1 . 5 . . . . . . . 3 . . . . 3 . . . . . 3 . 9 . 5 . 4 . . . 6 . 3 . 7 . . 3 1 . . . . . 9 8 . 6 . . . . . 5 . . . . . . . . . . . 5 . . . . . 6 . . . . . 6 . . . . . . 3 . 2 . 9 . . 5 9 . . . . . 3 4 . . 8 . . . 6 . . . 9 . 1 . 3 . 5 . . 5 . 6 . 1 . 8 . . . 7 . 6 . 8 . . . . . 1 . 5 . . . . . 4 . . . 2 . . . . 2 . . . 4 . . . . . . . . . . . 7 . . . . . . . 9 . . . . . . . . . . . . . . . . . . 81. Ano1 82. Ano1 83. Ano1 84. Ano1 . 1 . . . . . 5 . . . . . . . . . . . 2 . . . . . 5 . . 8 . . . . . 4 . . . . 3 . 7 . . . . 3 . 1 . 7 . 5 . . . . . 3 . . . . . . 5 . 7 . 9 . . . . . . 6 . . . . . . 2 . 6 . 8 . . . . . 1 . 6 . . . . 2 . . . . . 3 . . 8 . . . . . 4 . . 7 . . . . . 3 . . . 3 . 5 . 1 . . . . 9 . . . 5 . . . . 6 . . . 8 . . . . . . 9 . . . . . . . . 9 . . . . . . . 2 . 8 . . . . 5 . . 9 . . 1 . . . . 5 8 2 . . . 1 . 8 . . . 6 . 7 . . 1 . 6 . 7 . . . . 3 . . . 7 . . . . 8 . 2 . 9 . . . 9 . . 2 . . 4 . . . . 9 . 5 . . . . . . 1 . 8 . . . . 1 . . . . . 7 . . . 6 . . . 8 . . . . . . . . . . . . . 7 . . . 6 . . . . . . . . . . . . . . . . . . . . . 4 . . . . . 2 . 85. Ano1 86. olimpia 87. olimpia 88. olimpia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 5 . . . 3 . . 1 . 2 . . 5 4 . . . . . . . 7 . . . 2 . 4 . . . . . 2 . . . 6 . . . . 8 . . . 6 . . . 3 . . 1 . . 6 . 7 . . . . . . . 8 . 7 . . . . . 5 . . . 7 . . . 4 . . . . 2 . . . 5 . . 6 . . . 5 . . . 7 . . 4 . 9 . 2 . . . . . . 6 . . . . . . . . 3 . . . . . . 1 . 6 . 2 . . . 1 . . 6 . . 8 . . . . 5 . 3 . . . 9 . 8 . . . 2 . 4 . . 2 . . . 3 . . . . 6 . 2 . 9 . . . . 6 . 4 . 7 . . . . 5 2 . 4 8 . . . . 3 . . . 4 . . . 8 . . . . . 7 . 5 3 . . . . . 1 2 . 7 . . . . . 1 . 9 . . . 7 . . . 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . . . . 89. olimpia 90. olimpia 91. olimpia 92. olimpia 5 6 . . . . . 7 8 . . . 9 . 6 . . . . 1 . 2 . 3 . 4 . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 3 5 . . . . . . . 6 5 . . 1 . 3 . . 6 . . 2 . 1 . 3 . . 2 . . . . . . . 4 . . . . . . . . . . 4 . . 2 . . 8 . . . 4 . 3 . 2 . . 3 . . . . . . . 5 6 . . . 5 . . . 8 . . 3 . . . 6 . . . . . . . . . . . . 6 . 8 . 7 . 1 . . . . 4 . 2 . . . . . . . 4 . . . . . 7 . . . . . 8 . . 7 . . . . . 9 . 7 . . . . . . . 5 . 7 . . . . . 2 . . 4 . 7 . 8 . 5 . . 8 . . . . . 6 . . . . . 6 . . . . . . 6 5 . 1 3 . . . . . . . . . . . . . . . 3 . . . . 8 . . . . . . . 9 . 2 . . . . . 7 . . . 3 . . . 9 . . . . . . 4 . . . . . 4 . . . . . 1 . . . . . . . . . . 93. olimpia 94. olimpia 95. olimpia 96. olimpia . . . 2 . 3 . . . 3 . . . . . . . 2 . . . . 1 . . . . . . . 3 . 4 . . . 5 . . . 1 . . . 6 1 . . . 6 . . . 5 . 7 . . . . . 1 . 7 . . . . . . . 5 6 . . . . . . . 4 . 7 . . . . . 3 . . . 3 . . . 6 . . 8 . . . . . . . 1 7 . . . . . . . 5 . . 5 . . . 4 . . . . . . . . . . . . 9 . . . . . 3 . . . . . 2 . . . . . . . 2 . 3 . . . . . 6 2 . 3 8 . . . . 7 . 5 . 2 . . . 8 . . . . . 3 . . . . . 1 . . . . . 4 . . . . . 5 . . . . 8 . 6 . . . . 2 . . . . . 1 . . . . 5 . 4 . . . 6 . 8 . . . 2 . 3 1 . . . 7 . . . 8 . 3 . . . . . 9 . . 1 6 . . . 7 8 . . . . . 4 . . . . . 2 . . . . . 1 . . . . 4 . 5 . . . . . . . . . . . . . . 2 . . . 5 . . . . . . . . . . . 97. olimpia . . . 1 . 2 . . . 4 . . . . . . . 6 5 . . . . . . . 3 6 . . . 3 . . . 9 . . . . . . . . . . 7 . . 1 . . 8 . . 1 . . . . . 7 . . 8 . . . . . 2 . . . . 4 . 3 . . .

if anyone needs them in line format:

Code: Select all: .............1......1.2.3............4.....5..5.4.6.7...3...2....8...1...7.5.9.4. # 1. mauricio .............1......23.45.....2.6....4.....7..8.....1...3...6....5...2...1..8..4. # 2. mauricio ............1.2.....3...4.............4...5...1.6.7.2.....5.....2.....6.78..4..12 # 3. mauricio ............1.2.....3...4.............4...5...1.6.7.2.....5....2.......687..4..12 # 4. mauricio ............1.2.....3...4.............4.3.5...1.6.7.2....854....2.....1..9.....6. # 5. mauricio ............1.2.....3...4............1.5.6.2.2.4...7.1....3......8.4.6...5.....1. # 6. mauricio ............1.2.....3...4......5.....6.....7..7.....8...1...3....4.3.5...2.8.7.9. # 7. mauricio .5.....9..3.....6...47.82....2.3.4....7...1......5.......2.4....9.....3.......... # 8. olimpia ............2.3...8...1...9.32...56...6...3......4.......6.5...91.....74......... # 9. Rico Alan,R828-S11 ...........1.3.5.....2.4....2.....8...3.9.1......5.....4.6.8.2...5.7.9........... # 10. olimpia ............1.2.....1.3.4....4...1....5...3...2.6.7.8.....5.....7.....6..8.....2. # 11. mauricio,heart ..........9..1..3...6.2.7.....3.4...21.....98...........25.64...8.....1.......... # 12. Vic Reinhart,Raphael ..........7..1..6...9...2.....2.3...56.....18...........34.29...1..5..8.......... # 13. Vic Reinhart,Odyssey ....1.....5.....7...72.36...........81.....95...4.2.....3...2...9..5..1.......... # 14. Vic Reinhart,Electra ............1.2....34...56.....3....1.......77.......8...7.8....2.....4..6..5..3. # 15. mauricio .........12.....84.3.....7...4...6.....2.3.....5...9....6.9.5...7.....2.....5.... # 16. Rico Alan,R828-S09 ....1.....9..2..7...8...4.....3.4....1.....9.....7......45.63...2..9..1.......... # 17. Vic Reinhart,El Morro ...........8...3...4.2.7.6...........7.....4...3.1.8...2.6.4.7...5.3.1........... # 18. tarek ..........3..1..2...6...5...8..2..4...5...8......3......85.69...2..4..1.......... # 19. olimpia ...........1...2...3..4..5.....3......2...6....7...1.....1.6....5.....8..8.4.7.3. # 20. mauricio ....8....21.....343.......2.6.....5...8...9.....3.7.....5...6...........7...9...3 # 21. Rico Alan,R828-S12 ...........1...2...3..4..5.....3......6...7..2.8...1.6...1.8....4.....8..5.....2. # 22. mauricio 1.2...5.3....8....3.......4..9...2.....3.5....8.....6...........6..9..2.5.......1 # 23. Rico Alan,R828-S10 86.....145.......6....1.......8.2.....7...3.....6.4.....1.5.9...........4.......8 # 24. Vic Reinhart,Lulin ..........3..1..4...7...5......2......5...6...4..3..2.....4......85.69...1.....3. # 25. olimpia ..........6.....5...7.1.2......2.....7.....6...1.3.4......4.....8.5.6.9.2.......8 # 26. olimpia ....1....5...2...4.6.....5...7...2...8.5.6.7.....3......2.4.3...1.....6.......... # 27. olimpia 1...2...3.4.....5.............6.4...3.......12.......7....3.....8.....6..5.8.9.4. # 28. mauricio 1...2...3.4.....5.............6.4...2.......7..3...8.....2.5....5..7..9..6.....4. # 29. mauricio 1...2...3.4.5.6.7.............8.4.......3....9.......1....9.....5.....4..8..1..5. # 30. mauricio ....1........2......3...4......5......43.67...1.....8....4.7....2..8..1..8.....3. # 31. mauricio 1...2...3.4.....5.....1.......6.7...3.......18.......2.7.....4...........6.4.9.7. # 32. mauricio ...........1...2....23.45......6......3...1...6..7..8....5.2....8.....7.9.......6 # 33. mauricio 1.......2.3.4.5.6.............7.3...2.......58.......1....8.....6.....3..7..1..4. # 34. mauricio 1.......2.3.4.5.6.............7.6.....2...5..8.......1....8.....6.....3..7..1..4. # 35. mauricio ...........1...2...3.4.5.6.....1.....7.....3.36.....48....7.......3.6.....2...9.. # 36. mauricio ...........1...2...3.4.5.6.....1.....4.....3.6.......4...3.7.....2...1....8.9.7.. # 37. mauricio ....1......1...2....2...3.....2.3......4.5....6.....7...3...5...7..8..1..8.....6. # 38. mauricio 1...2...3.4.5.6.7.............8.7...3.......26.......1....6.....8.....4..7.....5. # 39. mauricio 1...2...3.4.....5....3.6......7.5...2.......13.......6....1.....8.....4..5.....7. # 40. mauricio 1.2...3.4.5.6.7.8.............5.8...3.......74.......1....3.....6.....5.....1.... # 41. mauricio 1.2...3.4.5.6.7.8.............5.8...3.......2..8...1......3.....6.....5.....1.... # 42. mauricio ....1.....4..2..3...7...5......3.....3..4..2...6...8.....5.6.....8...6...1.....4. # 43. olimpia ...........1.2.3...4.1.5.6.....7.....6.....4..8.....5....4.8.....7...2..3.......1 # 44. mauricio ...4.5...2.......1.3.....7...6...5.....2.3.......1........2......5...6...14...79. # 45. Vic Reinhart,Oaxaca ....1......2...3...4.....5....167.....3...4....8...5.....4.3...6.......19.......7 # 46. mauricio,spaceship ....8....13.....57.2.....3...4.6.9..............3.7.....8.4.6...5.....7.....9.... # 47. Rico Alan, R747-S13 81.....492.......1...5.7.....2.8.7....5...6......9.......6.3............1.......8 # 48. Rico Alan, Jade ..........3..1..2...6...5..7.......5.1..2..4.....3......85.67...2..4..1.......... # 49. olimpia ....1....4...2...883.....47..9...6.....3.4.......5......1.6.9...8.....3.......... # 50. olimpia ....1....84.....32.3.....8...1...2.....3.4.....5...3....6...5...7.....4.....2.... # 51. olimpia ...2.3...7...1...46.......55.......6..........7..2..9..2.....8..9.....3....5.4... # 52. olimpia ....1....5.......343.....65..7...1...5.3.4.8............2...9...6.....5.....2.... # 53. olimpia ....1....1.......92.......33.......7.7..6..5..8.5.2.6..6.....7....4.3............ # 54. olimpia ...7.3....1.....2....5.9.....5...9...6..4..1...3...6......6....9.7...5.4......... # 55. Ano1 ............1.5.....7...3...9..3..1...4.2.7...5..6..8...6.7.2...1.....9.......... # 56. Ano1 ...........4...6.....275.....6...1...3..5..9...9...4.....6.1....2.....3..5.....7. # 57. Ano1 ...........1...9...4.2.7.8.....9.......8.4.....5...1..87.....464.......2....5.... # 58. Ano1 ...........6...7.....1.3.....4.6.2.....9.8.....8...3...2.....1.1.......97...4...8 # 59. Ano1 ...9.6.....5...4.....4.8.....9.1.2.............7...8...4.....3.8.......6.6..3..7. # 60. Ano1 ............6.3.....5.7.2...9.....6...4.2.1...3.....8.7.2...5.4...3.8............ # 61. Ano1 ............4.2.....6.7.3.............1.6.7...9.....4.7.8...6.3.4.2.9.5.......... # 62. Ano1 ...........8...3...9.1.2.6.1...3...626.....79....8.......8.6.....7...4........... # 63. Ano1 ...........6.4.3...2.....7.97.....51.1.....9.....8.......5.1...4.3...8.2......... # 64. Ano1 .........8.9...6.4...5.1.......8.....5.....7...23948...7.....3.4.......9......... # 65. Ano1 ............2.1.....7...8...6.....5...5.7.3.....4.8.......8.....1.....9.82.....61 # 66. Ano1 ..........9.671.2...8...4.....845.......2.....1.....6...4.3.8...6.....7.......... # 67. Ano1 ...........7.3.5...8..7..2.9.3...7.1.6.4.2.8.............2.8.....9...3........... # 68. Ano1 ....5......3.8.9...5.....7...2...6.....3.1.....9...8.....896.......4.....1.....5. # 69. Ano1 ..........2..3..9...7.8.6......7......1.6.3...9.....2...6...8...4.5.2.1.......... # 70. Ano1 ............954....6.....7...........2.6.8.9...3.4.5.....7.2...5.4...3.1......... # 71. Ano1 ...428.............3.....7.4...9...1....5....1.8...6.4.5..7..3.8.......6......... # 72. Ano1 ..........3.....7....4.8.....4.9.1......5....8.1.3.4.6.5..7..3...8...6........... # 73. Ano1 ..........4.9.3.8...5...6...8.....5...2.6.7.....1.2.....6.5.1...9.....3.......... # 74. Ano1 ...........6...1...4.....2...32167...9.....4.....7.......9.5...1.7...6.3......... # 75. Ano1 ...........1...5...6.8.4.2.94.....828.......6....7.......2.6.....5.1.7........... # 76. Ano1 ...........8.7.6.....3.4.....2...7...3.9.5.4..........59.....34..7.6.8........... # 77. Ano1 ..........1.....2....678....2.....1...6.3.7...5.....6...8...6.....1.5...7.......9 # 78. Ano1 ...........2.4.6...8.....1.5.......331.....98....6.....9.1.3.5...4...2........... # 79. Ano1 .1.....6...4...3.....5.7.......3.....6.....5...3.2.9...5.6.1.8...2...4........... # 80. Ano1 .1.....5....3.7.......6.....8.....4...6...8...5..9..1...3...7.....1.8.....7...6.. # 81. Ano1 ..........3.1.7.5...2.6.8...7.....3.....9.......582.....8.2.9...1.....7.......... # 82. Ano1 .2.....5.....3.......1.6.....3.5.1......9....1.8...6.7.9..2..4...6...8........... # 83. Ano1 .8.....4...5.7.9...2.....3...9...5.....2.8.....1.6.7.....9.5.............4.....2. # 84. Ano1 ............785.....2...6...7.....5...4.9.2...1..6..8...6.2.9...8.....7.......... # 85. Ano1 .........3..1.2..5..8...6....7...4......6.......5.3.....6.4.7..53.....12......... # 86. olimpia, pattern 86 .........4.......7.3..1..6...2...5......3....9.8...2.4..52.48...7.....1.......... # 87. olimpia, pattern 87 ............2.4...7.......86...5...7..1.6.2....2...3....3...4..9...7...6....8.... # 88. olimpia, pattern 88 56.....78...........2.1.3....4.3.2............7.....8..4.7.8.5............3...9.. # 89. olimpia, pattern 89 ...9.6...1.......32.......43.......5.6.8.7.1..7.....9..8.....6.....3........4.... # 90. olimpia, pattern 90 .1.2.3.4.5.......6.........6...5...8...4.2...7.......5....6....8.......9.4.....1. # 91. olimpia, pattern 91 .........5..1.3..6.4..2..8...3...6......4.....7.....2...65.13...2.....7.......... # 92. olimpia, pattern 92 ...2.3...5...1...66.......47.......5....2.....8.....3..2.....1..3.....9....4.5... # 93. olimpia, pattern 93 3.......21...6...5.7.....3...5...4.....2.3.......1.......5.4....16...78.......... # 94. olimpia, pattern 94 ....1.....7.....1...3...6.............62.38...4.....5.6.8...2.3....4......2...5.. # 95. olimpia, pattern 95 ...3.4...7.......58.......1.9.....3...7.5.2.....8.6...1...7...8.2.....1.......... # 96. olimpia, pattern 96 ...1.2...4.......65.......36...3...9..........7..1..8..1.....7..8.....2....4.3... # 97. olimpia, pattern 97

Is there anyone willing to help find 3 more to make it an even 100 :roll:

by **olimpia** » Wed Aug 11, 2010 4:39 am

And, here's some trivia about the 97 unique shapes of sudokus with horizontal symmetry:

Only 2 have a box with this pattern:

Code: Select all: . X . . X . . X .

In both cases its a center box (patterns 56 and 73).

Only 3 have 5 consecutive clues in a row (or can be morphed into) such as:

Code: Select all: . . X X X X X . .

(patterns 65, 67, 75)

Several patterns have four clues within a box. Its always a center box isomorphic to:

Code: Select all: X . X . . . X . X

or

Code: Select all: . . . . X . X X X

but NEVER:

Code: Select all: . X . . X . X . X

NONE has diagonals within a box such as:

Code: Select all: X . . . . . . . X . X . . . . . X . . . X . . . X . .

And NONE has an empty middle column such as:

Code: Select all: . . . . . . . . .

Several have 1, 2, or 3 empty rows, and several have empty columns at the sides, but the middle column (C5) is never empty :!:

I would be interested in any speculation as to why there is never a diagonal within a box, or an empty middle column :roll:

Or is it just one of the many things about sudoku that has no explanation, its just is what it is :?:

And here I was able to find Pattern 98:

Code: Select all: . . . . . . . . . . 5 . . 1 . . 7 . . . 6 . . . 3 . . . . . . . . . . . 7 . . 3 . 4 . . 6 . 1 . . . . . 2 . . . 4 . . . 5 . . . . . . 2 . . . . 6 . 3 . . . 8 . 4

As with the others, no diagonals in a box, and no empty middle column :!:

The search goes on... :roll:

by **Serg** » Wed Aug 11, 2010 12:12 pm

olimpia,
you published very interesting results.
I think it is essential that no puzzles have empty central column (c5), because empty central column imposes additional symmetry constraints (more clues has to have symmetric twin-clues). I am very wondering too that no boxes have filled in 3 diagonal cells only.

Serg

by **eleven** » Wed Aug 18, 2010 10:13 am

olimpia wrote:Is there anyone willing to help find 3 more to make it an even 100

After you have found a new one it was easy, because very near to 2 puzzles in your list there are 2 more patterns:

Code: Select all: Near 18.tarek +-------+-------+-------+ | . . 1 | . . . | 8 . . | | . . 8 | . . . | 3 . . | | . . . | 2 . 7 | . . . | +-------+-------+-------+ | . . . | . . . | . . . | | . 7 . | . . . | . 4 . | | . . . | 5 1 8 | . . . | +-------+-------+-------+ | . 2 . | 6 . 4 | . 7 . | | . . 5 | . 3 . | 1 . . | | . . . | . . . | . . . | +-------+-------+-------+ Near 59. Ano1 +-------+-------+-------+ | . . . | . . . | . . . | | . . 1 | . . . | 9 . . | | . 4 . | 3 . 7 | . 8 . | +-------+-------+-------+ | . . . | . . . | . . . | | . . . | 4 9 8 | . . . | | . . 5 | . . . | 1 . . | +-------+-------+-------+ | 8 7 . | . . . | . 4 6 | | 4 . . | . . . | . . 2 | | . . . | . 5 . | . . . | +-------+-------+-------+

[Added:] This one looks nice

Code: Select all: . . . 4 . 5 . . . . 2 . . . . . 8 . . 3 . . . . . 7 . . . 6 . . . 5 . . . . . 2 9 3 . . . . . . . 1 . . . . . . . . 2 . . . . . . 5 . 8 . 6 . . . . 4 . . . 7 . . ..1...8....8...3.....2.7.............7.....4....518....2.6.4.7...5.3.1........... # 99. eleven ...........1...9...4.3.7.8....498..............5...1..87.....464.......2....5.... # 100. eleven ...4.5....2.....8..3.....7...6...5.....293.......1........2......5.8.6....4...7.. # 101. eleven

by **olimpia** » Fri Aug 20, 2010 12:14 am

eleven wrote:# 100. eleven

On March 10th, 1987, Hideaki Tomoyori recited pi to 40,000 decimal places.

On August 23, 2008, the Great Internet Mersenne Prime Search project discovered that 2^43,112,609 âˆ’ 1 is prime.

And on August 18, 2010, the 100th shape of an 18 clue sudoku with horizontal symmetry was discovered.

A job well done :!:

(and here is #102):

Code: Select all: . . . 1 . 2 . . . 9 . . . . . . . 4 8 . . . . . . . 1 5 . . . . . . . 6 . . . . . . . . . . . . 3 . 4 . . . . . 3 . 5 . 8 . . . 1 . . 6 . . 2 . . 2 . . . . . 3 . ...1.2...9.......48.......15.......6............3.4.....3.5.8...1..6..2..2.....3. # 102. olimpia

by **eleven** » Sun Aug 22, 2010 10:55 am

So i am happy to have thrown in my 2 (per)cents

olimpia wrote:A total of 97 have been discovered, and some people speculated that this may be near the total that exist.

Since the old posts are lost with the crash, this is, what my assumption was based on:
At that time ano1 has found 1.1 bio 18 clues. He estimated the total number to be 1.4. So he feared to spoil your fun, when publishing all the 70 (vertically) symmetric puzzles in his set. But it turned out, that you still found more and more.
Now my own estimate was i think 1.6 bio. So a simple calculation was, that we can expect about the same number of patterns in the unknown set of 18's as in the known one (relatively), minus the number of overlapping patterns (having puzzles in both sets).
This would give about 102 puzzles minus a big question mark, less than we have now.

Later ano1 calculated a much better estimate for the 19 clues (with the subset technique), which suggested, that my 18's estimate was too low (10 or 20 %). So now i think, that there should be maximum 127 - ?? puzzles.

Here are two more from the neighbourhood (i rearranged the puzzles you see in the compact form, as i got them, to look more pretty):

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . . | | 2 . 1 | . . . | 4 . 3 | | . 5 . | 7 . 6 | . 8 . | +-------+-------+-------+ | . . 4 | . . . | 9 . . | | . . . | 5 . 8 | . . . | | . . 3 | . 1 . | 2 . . | +-------+-------+-------+ | . 6 . | . . . | . 5 . | | . . . | . . . | . . . | | . . . | . 4 . | . . . | +-------+-------+-------+ +-------+-------+-------+ | . . . | . . . | . . . | | . . 1 | . 2 . | 9 . . | | . 4 . | 3 . 9 | . 8 . | +-------+-------+-------+ | . . . | 8 7 4 | . . . | | . . 5 | . . . | 1 . . | | . . . | . . . | . . . | +-------+-------+-------+ | . 8 . | . . . | . 2 . | | . 7 . | . 1 . | . 4 . | | . . . | . 5 . | . . . | +-------+-------+-------+ 1.2...3.4.5.7.6.8.............5.8...3...1...24.......9....4.....6.....5.......... #103 eleven ...........1.2.9...4.3.9.8.............874.....5...1...7..1..4..8.....2.....5.... #104 eleven

[Added:] one more

Code: Select all: . . . . . . . . . . . . 1 . 2 . . . . . 3 . . . 4 . . . . 4 . 3 . 5 . . . . 7 . . . 3 . . . . . 7 . 6 . . . . 1 . . 5 . . 7 . . 2 . . . . . 1 . . 9 . . . . . 6 . ...1.2..............3...4....7...3....4.3.5.....7.6....1..5..7..2.....1..9.....6. # 105. eleven

by **eleven** » Tue Aug 24, 2010 10:16 am

Thats all i found near the known puzzles. This does not mean much, e.g. i could not find olimpia's last puzzle near the others.

Totally i got 362 non equivalent symmetric puzzles. The most fruitful pattern seems to be #71 with 49 puzzles, followed by #77(24) and #79(20).

by **olimpia** » Wed Aug 25, 2010 12:40 am

eleven wrote:The most fruitful pattern seems to be #71 with 49 puzzles, followed by #77(24) and #79(20).

Thanks for the stats. It's interesting that #71 is the most fruitful, but not among the first to be discovered. (after about the first 50, the list is in the order of discovery <posted> although the first half may not be in order). And Ano1's were from a huge list of general 18s, and he culled out the symmetric ones in one big sweep.

(also, I previously wrote:)

olimpia wrote:Only 2 have a box with this pattern:
Code: Select all
. X . . X . . X .
In both cases its a center box (patterns 56 and 73).

Then...

eleven wrote: . . . . . . . . .
. . . 1 . 2 . . .
. . 3 . . . 4 . .
. . 4 . 3 . 5 . .
. . 7 . . . 3 . .
. . . 7 . 6 . . .
. 1 . . 5 . . 7 .
. 2 . . . . . 1 .
. 9 . . . . . 6 .

(# 105. eleven)

(sorry, i'm showing without code to add the red hi-lite)

Good work :!:

by **eleven** » Sat Aug 28, 2010 10:25 pm

olimpia wrote:NONE has diagonals within a box such as:
Code: Select all
X . . . . . . . X . X . . . . . X . . . X . . . X . .

As we know, a mini-diagonal is a very weak pattern for solvers.

In low clue puzzles you almost waste a given, because you need 3 other numbers to produce a single in this box, the same as for 2 clues in the diagonal.
And it only contributes a single number for a row/column.
A mini-column also needs 3 numbers for a single in its box, but it exludes 3 numbers in the rest of this column, which can be a big help (when you solve my last puzzle, you can observe that).

So its no surprise that puzzles with mini-diagonals in the diagonal boxes can be extremely difficult. Most of the hardest known puzzles have a very similar pattern.

by **olimpia** » Sat Sep 18, 2010 4:01 pm

Serg wrote:you published very interesting results.
I think it is essential that no puzzles have empty central column (c5), because empty central column imposes additional symmetry constraints (more clues has to have symmetric twin-clues). I am very wondering too that no boxes have filled in 3 diagonal cells only.

Thanks Serg, good point. In fact some of the 18s I made were by adjusting the position of the clues in C5 where they can be anywhere in C5. All the other clue postions cannot be moved, unless you move them two at a time.

eleven wrote:As we know, a mini-diagonal is a very weak pattern for solvers.
In low clue puzzles you almost waste a given, because you need 3 other numbers to produce a single in this box, the same as for 2 clues in the diagonal.
And it only contributes a single number for a row/column.
A mini-column also needs 3 numbers for a single in its box, but it exludes 3 numbers in the rest of this column, which can be a big help (when you solve my last puzzle, you can observe that).

Thanks Eleven. Thats a good explanation why mini-diagonals doesn't exist (or not discovered).

I keep thinking that if just one clue next to the diagonal could be resolved (such as this):

Code: Select all: X . . X X . . . X

then it would be a big help to resolve the rest of the grid, but I guess it just never happens. One reason I think is that when placing 18 random clues on a 9x9 grid its almost always near-dead right away - that is only a very small percentage go beyond solving even just 2 or 3 more positions. So I think that's why your theory prevails.

In just two cases I have found a pattern with mini-diagonals that makes 3 solutions. One example is this:

Code: Select all: (non valid grid/ 3 solutions) X . . . . . . . X . X . X . X . X . . . X . X . X . . . X . . . . . X . . . X . X . X . . . . . . . . . . . . X . . . . . X . . . . . X . . . . . . . . X . . . . 6.......5.2.6.4.1...7.1.8...1.....6...3.8.7............4.....2.....3........7....

OK, I'll keep looking for more of these 18s. I'll write back next September (2011) or sooner if I find anything

by **Serg** » Fri Apr 22, 2011 7:19 am

[Edited: post deleted, because it was contained wrong results]
Serg

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