## Symmetric 18s

Everything about Sudoku that doesn't fit in one of the other sections

### Re: Symmetric 18s

eleven wrote: How many 19's do you have so far ?

probably more than 200,000.
unfortunately i dont know how many individual patterns [19clues with 3 clues in column5] i have gone through.
i suppose i perform a successive --similar 2 with gridchecker until it fizzles out.
Taking a symmetrical 19 and doing a selective {-2} to give a symmetrical 17subpuzzle and then {+2] potentially gives new patterns, but this is slow.

C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Hi, coloin!
I confirm that your last pattern (#113) is new unique 18-clue sym. pattern. (Published puzzle is minimal.)
It turns out, that you discovered pattern beloning to new distribution, not observed earlier. (Sym. 18-clue patterns having empty box are rare, 4 such patterns are observed only.) Congratulations!

Moreover, this new distribution (011222334) is lowest in sym. 18-clue patterns distribution list. So, you expanded limits of known sym. 18-clue patterns! Well done!

Serg
Serg
2018 Supporter

Posts: 627
Joined: 01 June 2010
Location: Russia

### Re: Symmetric 18s

Code: Select all
`+---+---+---+|.1.|...|.2.||.3.|...|.4.||...|567|...|+---+---+---+|..1|...|7..||...|3.2|...||...|.4.|...|+---+---+---+|...|2.1|...||..7|...|6..||..5|...|8..|+---+---+---+.1.....2..3.....4....567.....1...7.....3.2.......4.......2.1.....7...6....5...8.. # 114  coloin `

There cant be many left to find now
C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Hi, coloin!
coloin wrote:
Code: Select all
`.1.....2..3.....4....567.....1...7.....3.2.......4.......2.1.....7...6....5...8.. # 114  coloin `

I confirm that you've found new 18-clue vertically symmetric pattern. Congratulations!
Published puzzle is minimal.

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

Nice configuration! It resembles me a cat (or armchair). This is why I like sym. puzzles.

Serg

[Edited. I added "natural" representation of the puzzle #114.]
Serg
2018 Supporter

Posts: 627
Joined: 01 June 2010
Location: Russia

### Re: Symmetric 18s

Nice equivalent pattern, there are many pretty ones for this puzzle, e.g.
Code: Select all
` +-------------------+ | . . 4 . . . 5 . . | | . . . 2 . 3 . . . | | . . . . 1 . . . . | | . . . 3 . 4 . . . | | . . 5 . . . 6 . . | | . . 7 . . . 8 . . | | . . . 7 6 5 . . . | | 2 . . . . . . . 1 | | 4 . . . . . . . 3 | +-------------------+`

Congrats on another one, Coloin. This one has 9 known ones in {-5+5}.
coloin wrote:There cant be many left to find now

So your 19 collection does not grow much any longer?

Here's my update.
Posted:
Hidden Text: Show
.............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
.........4.......7.3..1..6...2...5......3....9.8...2.4..52.48...7.....1.......... # 87. olimpia
............2.4...7.......86...5...7..1.6.2....2...3....3...4..9...7...6....8.... # 88. olimpia
56.....78...........2.1.3....4.3.2............7.....8..4.7.8.5............3...9.. # 89. olimpia
...9.6...1.......32.......43.......5.6.8.7.1..7.....9..8.....6.....3........4.... # 90. olimpia
.1.2.3.4.5.......6.........6...5...8...4.2...7.......5....6....8.......9.4.....1. # 91. olimpia
.........5..1.3..6.4..2..8...3...6......4.....7.....2...65.13...2.....7.......... # 92. olimpia
...2.3...5...1...66.......47.......5....2.....8.....3..2.....1..3.....9....4.5... # 93. olimpia
3.......21...6...5.7.....3...5...4.....2.3.......1.......5.4....16...78.......... # 94. olimpia
....1.....7.....1...3...6.............62.38...4.....5.6.8...2.3....4......2...5.. # 95. olimpia
...3.4...7.......58.......1.9.....3...7.5.2.....8.6...1...7...8.2.....1.......... # 96. olimpia
...1.2...4.......65.......36...3...9..........7..1..8..1.....7..8.....2....4.3... # 97. olimpia
..........5..1..7...6...3...........7..3.4..6.1.....2...4...5......2....6.3...8.4 # 98. olimpia
..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
...1.2...9.......48.......15.......6............3.4.....3.5.8...1..6..2..2.....3. # 102. olimpia
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
...1.2..............3...4....7...3....4.3.5.....7.6....1..5..7..2.....1..9.....6. # 105. eleven
1.......32.......4..78.46....6...9...........5...3...13.......2....1.......9.8... # 106. olimpia
...........3...5..6..7.9..1.........9...4...71...5...9...6.1.....5...3...4.....8. # 107. eleven
....1......2...3....4.5.6.....6.3.....6...2...7.....8....4.2....9.....1.5.......7 # 108. eleven
............123.....4...5.....4.5....3.....1.2.......6..5...7....7.8.9...1.....2. # 109. eleven
...........1...2...3..4..5....1.5.....6...7..2.......4...726....5.....8..1.....3. # 110. eleven
............1.2....32...45.....4....6.......78...3...1...6.7.....5...2....4...9.. # 111. coloin
....1......2...3...1.4.5.6...........2.....5..4..6..1....3.2.....3...7..7.......8 # 112. coloin
..........1.2.3.4...5...6.....657....3.....8.....9......9...2....6...5...2.....3. # 113. coloin
.1.....2..3.....4....567.....1...7.....3.2.......4.......2.1.....7...6....5...8.. # 114. coloin

Patterns sorted:
Hidden Text: Show
.............1......1...1.............11.11..11.....11...1.1....1.....1..1..1..1. # 103. eleven
.............1......1.1.1............1.....1..1.1.1.1...1...1....1...1...1.1.1.1. # 1. mauricio
.............1......11.11.....1.1....1.....1..1.....1...1...1....1...1...1..1..1. # 2. mauricio
.............1.....11...11....1.1......1.1...1.......1..1...1....1...1..1...1...1 # 55. Ano1
............1.1.....1...1.............1...1...1.1.1.1.....1.....1.....1.11..1..11 # 3. mauricio
............1.1.....1...1.............1...1...1.1.1.1.....1....1.......111..1..11 # 4. mauricio
............1.1.....1...1.............1...1...1.1.1.1.....1....1...1...111.....11 # 63. Ano1
............1.1.....1...1.............1.1.1...1.....1.....1.....1..1..1.11..1..11 # 73. Ano1
............1.1.....1...1.............1.1.1...1.....1...1.1.1...1..1..1..1..1..1. # 56. Ano1
............1.1.....1...1.............1.1.1...1..1..1...........1.1.1.1.1.1...1.1 # 68. Ano1
............1.1.....1...1.............1.1.1...1.1.1.1....111....1.....1..1.....1. # 5. mauricio
............1.1.....1...1............1.1.1.1.1.1...1.1....1......1.1.1...1.....1. # 6. mauricio
............1.1.....1...1......1......1.1.1...1.....1...1.1.1...1.....1..1..1..1. # 88. olimpia
............1.1.....1...1......1.....1.....1..1.....1...1...1....1.1.1...1.1.1.1. # 7. mauricio
............1.1.....1...1......1.....1.....1..1.....1...1.1.1....11.11...1.....1. # 54. olimpia
............1.1.....1...1......1.....1.....1..1..1..1....1.1.....1...1..1.1...1.1 # 48. Rico Alan, Jade
............1.1.....1...1......1.....1.....1..1..1..1...1...1....1...1...1.1.1.1. # 8. olimpia
............1.1.....1...1......1.....1.....1.11.....11...1.1.....1.1.1...1.....1. # 66. Ano1
............1.1.....1...1.....1.1.....1...1....1...1...1.....1..1..1..1.1...1...1 # 102. olimpia
............1.1.....1...1.....1.1.....1...1....1.1.1...1.....1..1.....1..1..1..1. # 105. eleven
............1.1.....1...1.....1.1.....1...1....1.1.1...1.....1..1..1..1.1.......1 # 59. Ano1
............1.1.....1...1.....1.1....1.....1..1..1..1...1...1....1...1...1..1..1. # 84. Ano1
............1.1.....1.1.1..............1.1....11...11.....1....1.......111.....11 # 9. Rico Alan,R828-S11
............1.1.....1.1.1..............1.1....11...11...1.1.1..1.......11.......1 # 61. Ano1
............1.1.....1.1.1.............1...1...1.1.1.1............1.1.1..11.....11 # 77. Ano1
............1.1.....1.1.1.............1...1...1.1.1.1.....1....1.......111.....11 # 76. Ano1
............1.1.....1.1.1.............1.1.1...1.....1...........1.1.1.1.1.1...1.1 # 62. Ano1
............1.1.....1.1.1.............1.1.1...1.1.1.1.....1......1.1.1...1.....1. # 10. olimpia
............1.1.....1.1.1......1......1.1.1...1.....1.....1.....1.....1.11.....11 # 47. Rico Alan, R747-S13
............1.1.....1.1.1......1.....1.....1..1.....1...1...1....1...1...1.1.1.1. # 11. mauricio,heart
............1.1....11...11.............111...1.......1...........1.1.1..1..1.1..1 # 71. Ano1
............1.1....11...11............1...1..1.......1....1......11111..1.......1 # 75. Ano1
............1.1....11...11............1...1..1.......1....1.....1.111.1.1.......1 # 65. Ano1
............1.1....11...11............1...1..1..1.1..1...........1.1.1..1...1...1 # 12. Vic Reinhart,Raphael
............1.1....11...11............1.1.1..1.......1...........1.1.1..1..1.1..1 # 13. Vic Reinhart,Odyssey
............1.1....11...11............1.1.1..1.......1....1......1...1..1..1.1..1 # 14. Vic Reinhart,Electra
............1.1....11...11............1.1.1..1.......1....1....1.......111.....11 # 64. Ano1
............1.1....11...11.....1.......1.1.....1...1...1.....1.1.......11...1...1 # 94. olimpia
............1.1....11...11.....1....1.......11.......1...1.1.....1...1....1.1.1.. # 15. mauricio
............1.1....11...11.....1....1.......11...1...1...1.1.....1...1....1...1.. # 111. coloin
............111.....1...1.............1...1...1.1.1.1.....1....1.......111.....11 # 100. eleven
............111.....1...1.............1.1.1...1.....1.....1.....1..1..1.11.....11 # 72. Ano1
............111.....1...1.............1.1.1...1.....1...1.1.1...1.....1..1..1..1. # 85. Ano1
............111.....1...1.............1.1.1...1.1.1.1.....1.....1.....1..1..1..1. # 104. eleven
............111.....1...1.............11.11...1..1..1....1.1....1.....1..1.....1. # 99. eleven
............111.....1...1.....1.1....1.....1..1.....1...1...1....1...1...1..1..1. # 57. Ano1
............111.....1...1.....1.1....1.....1.1.......1..1...1....1...1...1..1..1. # 78. Ano1
............111.....1...1.....1.1....1.....1.1.......1..1...1....1.1.1...1.....1. # 109. eleven
...........1...1....1.1.1......1......11.11...1.....1....1.1....1.....1.1.......1 # 112. coloin
...........1...1....1.1.1.....1.1......1.1.....1...1...1.....1..1..1..1.1.......1 # 60. Ano1
...........1...1....11.11......1......1...1...1..1..1....1.1....1.....1..1.....1. # 32. mauricio
...........1...1....11.11......1......1...1...1..1..1....1.1....1.....1.1.......1 # 33. mauricio
...........1...1...1..1..1............11.11...1.....1............11.11...1..1..1. # 18. tarek
...........1...1...1..1..1............11.11...1.....1...........1..1..1.1.1...1.1 # 89. olimpia
...........1...1...1..1..1............11.11...1.....1.....1....1.......11.1...1.1 # 79. Ano1
...........1...1...1..1..1............11.11...1.....1....1.1.....1...1...1..1..1. # 74. Ano1
...........1...1...1..1..1............11.11...1..1..1.....1.......111.....1...1.. # 82. Ano1
...........1...1...1..1..1............11.11...1..1..1.....1......1...1...1..1..1. # 19. olimpia
...........1...1...1..1..1............11.11...1..1..1.....1.....1..1..1.1.......1 # 49. olimpia
...........1...1...1..1..1............11111...1.....1.....1.......111.....1...1.. # 67. Ano1
...........1...1...1..1..1...........1.....1.1..1.1..1....1......1...1..1.1...1.1 # 98. olimpia
...........1...1...1..1..1...........1.....1.1..1.1..1....1....1.......11.1...1.1 # 87. olimpia
...........1...1...1..1..1.....1.......1.1....1.....1.....1......1.1.1..1.1...1.1 # 83. Ano1
...........1...1...1..1..1.....1.......1.1....1.....1.....1....1...1...11.1...1.1 # 50. olimpia
...........1...1...1..1..1.....1.......1.1....1.....1...11.11...1.....1..1.....1. # 106. olimpia
...........1...1...1..1..1.....1......1...1....1...1.....1.1....1.....1..1.1.1.1. # 20. mauricio
...........1...1...1..1..1.....1......1...1....11.11.....1.1....1.....1..1.....1. # 28. mauricio
...........1...1...1..1..1.....1......1...1...1..1..1.....1......11.11...1.....1. # 25. olimpia
...........1...1...1..1..1.....1......1...1...1..1..1.....1......11.11..1.......1 # 26. olimpia
...........1...1...1..1..1.....1......1...1..1...1...1....1......11.11...1.....1. # 27. olimpia
...........1...1...1..1..1.....1......1...1..1.1...1.1...1.1......1.1....1.....1. # 24. Vic Reinhart,Lulin
...........1...1...1..1..1.....1......1...1..1.1...1.1...1.1....1.....1..1.....1. # 22. mauricio
...........1...1...1..1..1.....1......1...1..1.1...1.1...1.1....1.....1.1.......1 # 23. Rico Alan,R828-S1.
...........1...1...1..1..1.....1.....1.....1.11.....11...1.1.....1...1..1.......1 # 21. Rico Alan,R828-S12
...........1...1...1..1..1....1.1.....1...1....1.1.1.....1.1....1.....1..1.....1. # 52. olimpia
...........1...1...1..1..1....1.1.....1...1....1.1.1.....1.1....1.....1.1.......1 # 29. mauricio
...........1...1...1..1..1....1.1.....1...1..1.......1...111....1.....1..1.....1. # 110. eleven
...........1...1...1..1..1....1.1.....1...1..1...1...1...1.1....1.....1..1.....1. # 96. olimpia
...........1...1...1.1.1.1............1.1.1...1..1..1.....1......1.1.1...1.....1. # 70. Ano1
...........1...1...1.1.1.1............1.1.1..1..1.1..1....1......1...1...1.....1. # 92. olimpia
...........1...1...1.1.1.1............1.1.1..11.....11....1.......1.1.....1...1.. # 86. olimpia
...........1...1...1.1.1.1...........1..1..1..1..1..1....1.1.....1...1..1.......1 # 107. eleven
...........1...1...1.1.1.1.....1.......1.1.....1...1......1.....1.....1.11.....11 # 36. mauricio
...........1...1...1.1.1.1.....1.......1.1.....1...1......1....1.......111.....11 # 58. Ano1
...........1...1...1.1.1.1.....1.......111....1.....1...1...1....1...1...1.....1. # 113. coloin
...........1...1...1.1.1.1.....1......1...1...1.....1.....1.....1.....1.11.....11 # 95. olimpia
...........1...1...1.1.1.1.....1......1...1...1.....1.....1....1.......111.....11 # 53. olimpia
...........1...1...1.1.1.1.....1......1...1...1.....1....1.1.....1...1....1.1.1.. # 91. olimpia
...........1...1...1.1.1.1.....1......1.1.1...1.....1....1.1.....1...1...1.....1. # 80. Ano1
...........1...1...1.1.1.1.....1.....1.....1..1..1..1....1.1.....1...1....1...1.. # 34. mauricio
...........1...1...1.1.1.1.....1.....1.....1..1..1..1....1.1.....1...1..1.......1 # 35. mauricio
...........1...1...1.1.1.1.....1.....1.....1.1.......1...1.1.....1...1....1.1.1.. # 37. mauricio
...........1...1...11...11.....1......1...1..1...1...1...1.1...1.......11.......1 # 16. Rico Alan,R828-S.9
...........1.1.1...1..1..1....1.1.....1...1....1...1.....1.1....1.....1..1.....1. # 97. olimpia
...........1.1.1...1.1.1.1.....1.......1.1.....1...1......1......1.1.1...1.....1. # 17. Vic Reinhart,El Morro
...........1.1.1...1.1.1.1.....1.......1.1.....1...1......1.....1.....1..1..1..1. # 30. mauricio
...........1.1.1...1.1.1.1.....1.....1.....1..1.....1....1.1.....1...1....1...1.. # 39. mauricio
...........1.1.1...1.1.1.1.....1.....1.....1..1.....1....1.1.....1...1..1.......1 # 44. mauricio
...........11.11..11.....11....1........1......1...1.....1.1....1.....1..1.....1. # 41. mauricio
...........11.11..11.....11....1........1......1...1.....1.1....1.....1.1.......1 # 42. mauricio
....1........1......1...1......1......11.11...1.....1....1.1....1.....1..1..1..1. # 31. mauricio
....1........1......1...1.....1.1....1.....1..1.....1...1...1....11.11...1.....1. # 90. olimpia
....1.......1.1.....1...1......1......1...1...11...11....1.1....1.....1.1.......1 # 45. Vic Reinhart,Oaxaca
....1.......1.1.....1...1.....1.1.....1...1....1...1.....111....1.....1..1.....1. # 114. coloin
....1.......1.1.....1...1.....1.1....1.....1..1.....1...1...1....1.1.1...1.....1. # 81. Ano1
....1.......111.....1...1......1......1...1....1.1.1.....1.1....1.....1..1.....1. # 101. eleven
....1.......111.....1...1......1......1...1...1..1..1....1.1....1.....1..1.....1. # 69. Ano1
....1......1...1....1...1.....1.1......1.1....1.....1...1...1...1.....1..1..1..1. # 38. mauricio
....1......1...1....1...1.....1.1.....1...1...1..1..1....1.1....1.....1..1.....1. # 40. mauricio
....1......1...1....1.1.1.....1.1.....1...1...1.....1....1.1....1.....1.1.......1 # 108. eleven
....1......1...1...1.....1.....1......1...1..1.1...1.1...1.1....1.....1..1.....1. # 51. olimpia
....1......1...1...1.....1....1.1.....1...1....1...1.....1.1....1.....1..1..1..1. # 93. olimpia
....1......1...1...1.....1....1.1...1.......11.......1...111.....1...1....1...1.. # 46. mauricio,spaceship
....1......1...1...1..1..1.....1......1...1...1..1..1....1.1.....1...1...1.....1. # 43. olimpia

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...........1.2.3...4.1.5.6.....7.....5.....8..6.....9....6.9.....3...1....7...2..
...........1.2.3...3.4.5.6.....7.....4.....3..6.....8....8.6.....2...9....7...1..
...........1.2.3...4.5.6.7.....5.....6.....4..7.....8....4.8.....2...1....3...5..
...........1.2.3...4.1.5.6.....7.....6.....4..8.....5....4.8.....7...2..3.......1
...........1.2.3...4.1.5.6.....7.....6.....4..8.....5....8.4.....7...2..3.......1
...........12.34..25.....67....6........8......4...3.....1.4....6.....5..9.....8.
...........12.34..25.....67....5........6......3...1.....1.4....6.....8..7.....5.
...........12.34..52.....67....6........8......4...3.....4.1....6.....5..9.....8.
...........12.34..56.....78....5........7......2...1.....4.1....4.....5..7.....6.
...........12.34..56.....78....5........7......4...2.....4.1....7.....3..8.....5.
...........12.34..56.....78....5........7......4...2.....4.1....3.....5..7.....6.
...........12.34..56.....78....5........7......4...2.....1.4....3.....5..7.....6.
...........12.34..56.....78....5........7......4...2.....4.1....7.....6..8.....3.
...........12.34..56.....78....5........7......2...1.....1.4....4.....5..7.....6.
...........12.34..56.....78....5........8......2...1.....1.4....8.....6.9.......5
...........12.34..56.....78....5........8......2...1.....1.4....7.....5.8.......3
...........12.34..56.....78....5........7......2...1.....4.1....4.....5.7.......6
...........12.34..56.....78....5........7......2...1.....1.4....4.....5.7.......6
...........12.34..56.....78....5........8......2...1.....4.1....4.....6.7.......5
....1........2......3...4......5......43.67...1.....8....4.7....8.....3..2..8..1.
....1........2......3...4.....3.5....1.....6..2.....7...5...8....68.43...9.....1.
....1........2......3...4.....3.5....1.....6..2.....7...5...8....68.43...9.....2.
....1.......2.3.....4...5......2......5...4...16...78....6.5....3.....7.2.......1
....1.......2.3.....4...5.....3.4.....5...6....7...8.....765....2.....1..4.....3.
....1.......2.3.....4...5.....4.6....2.....3..3.....1...6...7....5.8.4...1.....6.
....1.......2.3.....4...5.....4.6....2.....1..3.....2...5...7....6.8.4...1.....5.
....1.......234.....5...6......2......7...8....6.9.5.....7.6....2.....9..4.....8.
....1.......234.....5...6......5......7...5...3..2..8....8.6....2.....3..4.....9.
....1.......234.....5...6......7......6...8...2..4..3....8.5....7.....4..9.....2.
....1......1...2....2...3.....2.3......4.5....6.....7...3...5...8.....6..7..8..1.
....1......1...2....2...3.....2.4......5.3....6.....7...3...4...8.....6..7..8..1.
....1......2...3....3...4.....2.3......5.6....7.....8...5...2...8.....7..1..4..9.
....1......2...3....3...4.....2.4......3.5....6.....7...4...8...9.....1..7..8..6.
....1......2...3....3...4.....2.3......5.6....4.....7...5...2...7.....1..1..8..9.
....1......2...3....3...4.....2.5......6.3....4.....7...6...2...7.....1..1..8..9.
....1......2...3....3...4.....2.5......6.3....7.....8...6...2...8.....7..1..4..9.
....1......2...3....4...5.....2.4......5.6....7.....8...5...2...3.....1..8..9..5.
....1......2...3....4...5.....1.6.....3...4...6..7..8....3.2....7.....1..8.....6.
....1......2...3....4...5.....6.7.....3...4...1..8..6....5.4....6.....7..8.....1.
....1......2...3....4...5.....6.7.....3...4...6..8..7....2.3....1.....8..7.....6.
....1......2...3....4.5.6.....2.4.....3...4...7.....8....3.6....1.....9.8.......5
....1......2...3....4.5.6.....2.4.....6...4...7.....8....3.6....1.....9.8.......5
....1......2...3...4.....5.....6......3...7..1.5...2.8...2.7....6.....1..9.....4.
....1......2...3...4.....5.....6......7...8..1.8...2.7...2.8....1.....6..8.....4.
....1......2...3...4.....5.....6......7...8..1.8...9.2...8.9....1.....6..8.....4.
....1......2...3...4.....5....4.6.....7...1....8...2.....2.1....6.....9..9..7..4.
....1......2...3...4.....5....2.5...1.......67.......8...761.....4...9....5...2..
....1......2...3...4.....5....4.6...7.......18.......9...971.....3...5....6...4..
....1......2...3...4.....5....4.6...7.......18.......9...179.....3...5....6...4..
....1......2...3...4.....5....2.6...7.......18.......9...971.....3...5....6...2..
....1......2...3...1..4..5.....6......7...8...4..5..1....2.8.....3...2...6.....4.
eleven

Posts: 2013
Joined: 10 February 2008

### Re: Symmetric 18s

My 19 collection is still increasing ..... maybe half a million now.
Came back from holiday to this new one
Code: Select all
`+---+---+---+|...|.1.|...||..2|...|3..||.4.|...|.5.|+---+---+---+|..6|...|7..||...|8.9|...||..9|...|2..|+---+---+---+|.5.|.7.|.4.||.8.|...|.9.||1..|...|..5|+---+---+---+....1......2...3...4.....5...6...7.....8.9.....9...2...5..7..4..8.....9.1.......5 # 115 coloin`

C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Hi, coloin!
coloin wrote:....1......2...3...4.....5...6...7.....8.9.....9...2...5..7..4..8.....9.1.......5 # 115 coloin

I confirm that you've found new 18-clue vertically symmetric pattern. Congratulations!
Published puzzle is minimal.

This is "natural" view of the puzzle:
Code: Select all
`. . . . 1 . . . .. . 2 . . . 3 . .. 4 . . . . . 5 .. . 6 . . . 7 . .. . . 8 . 9 . . .. . 9 . . . 2 . .. 5 . . 7 . . 4 .. 8 . . . . . 9 .1 . . . . . . . 5`

Nice configuration! It resembles me russian church.
How many new sym. 18-clue patterns are you expecting to find else?

Serg
Serg
2018 Supporter

Posts: 627
Joined: 01 June 2010
Location: Russia

### Re: Symmetric 18s

Serg wrote:How many new sym. 18-clue patterns are you expecting to find else?

thinking about it .... depending on the number of clues in column 5 [2 or 4] the number of symmetric 19 patterns is x7 and x5 respectively the symmetric 18 patterns.
i dont think i have searched 19 patterns with only one clue in column 5.

i dont know how many of the 19 patterns i have gone through - i am still finding new 19 patterns - so it is impossible to know if there will still be new puzzles undiscovered.......

C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Finally - another one - like no other !

Code: Select all
`1.......2............345......162..............3...4...34...78...5...3.....6.1... # 116  coloin `

Code: Select all
`+---+---+---+|1..|...|..2||...|...|...||...|345|...|+---+---+---+|...|162|...||...|...|...||..3|...|4..|+---+---+---+|.34|...|78.||..5|...|3..||...|6.1|...|+---+---+---+`

Like all the recent additions it has 2 clues in c5

It looks like we have found all the puzzles of the previous 115 patterns.

6 clues in c5 would appear impossible - i have been unable to find 19 clue symmetrical puzzles with 7 clues in c5

No clues in c5 would also appear to be a no-no. I have been able to find 19 clue symmetrical puzzles with 1 clue in c5 - but as mentioned before there seems to be a requirement to always need this clue.

C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Congratulations!
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: Symmetric 18s

Hi, coloin!
coloin wrote:
Code: Select all
`1.......2............345......162..............3...4...34...78...5...3.....6.1... # 116  coloin`

I confirm that you've found new 18-clue vertically symmetric pattern. Congratulations!
Published puzzle is minimal. You found the first pattern having distribution 111123333 (distribution of clues over boxes)! Well done!
Moreover, this new pattern has a few unique properties. It is unique pattern having 4 boxes containing 1 clue. It is unique pattern having 4 boxes containing 3 clues. It is unique pattern having 1 box only containing 2 clues.

This is "natural" view of the puzzle:
Code: Select all
`1 . . . . . . . 2. . . . . . . . .. . . 3 4 5 . . .. . . 1 6 2 . . .. . . . . . . . .. . 3 . . . 4 . .. 3 4 . . . 7 8 .. . 5 . . . 3 . .. . . 6 . 1 . . .`

Is it a jug?

Concerning possible number of clues in the central (c5) column.

Let me cite my own previous post in this thread (see my post), where I calculated possible number of symmetric 18-clue patterns (simple combinatorial calculations):
Code: Select all
`Column c5 contains 0 clues:   94143280 patterns ( 4  %)Column c5 contains 2 clues: 1089372240 patterns (45  %)Column c5 contains 4 clues: 1051807680 patterns (44  %)Column c5 contains 6 clues:  163614528 patterns ( 7  %)Column c5 contains 8 clues:    3392928 patterns ( 0.1%)`

I processed all 188268 "filtered out" patterns (filtered eleven's list of all possible essentially different sym. 18-clue patterns) and found such statistics:
Code: Select all
`Column c5 contains 0 clues:   6937 patterns ( 4  %)Column c5 contains 2 clues:  81200 patterns (43  %)Column c5 contains 4 clues:  85353 patterns (45  %)Column c5 contains 6 clues:  14548 patterns ( 8  %)Column c5 contains 8 clues:    230 patterns ( 0.1%)`

So, you can see, no variants of possible number of clues in the central column can be excluded yet.

This is statistics for observed patterns:
Code: Select all
`Column c5 contains 0 clues:   0 patternsColumn c5 contains 2 clues:  92 patterns (79 %)Column c5 contains 4 clues:  24 patterns (21 %)Column c5 contains 6 clues:   0 patternsColumn c5 contains 8 clues:   0 patterns`

As you can see, no patterns having 0, 6 or 8 clues in c5 column were observed yet.

Serg

[Edited: I shortened representation of number of patterns for different central column's configurations.]
Serg
2018 Supporter

Posts: 627
Joined: 01 June 2010
Location: Russia

### Re: Symmetric 18s

Ive just had a look at this pattern .....and it doesnt appear to have valid puzzles
Code: Select all
`+---+---+---+|xxx|xxx|xxx||...|.x.|...||...|.x.|...|+---+---+---+|xxx|.x.|xxx||xxx|.x.|xxx||xxx|.x.|xxx|+---+---+---+|xxx|.x.|xxx||xxx|.x.|xxx||xxx|.x.|xxx|+---+---+---+ `

maybe more possible templates can be excluded - should we be able to prove it.....
C
coloin

Posts: 1749
Joined: 05 May 2005

### Re: Symmetric 18s

Hi coloin,
You might collaborate with Serg who 20 days ago identified that pattern P36 has no valid puzzles.
Your pattern is a symmetric extension to this morph of the former
Code: Select all
`+---+---+---+|xxx|xxx|...||...|.x.|...||...|.x.|...|+---+---+---+|xxx|.x.|xxx||xxx|.x.|xxx||xxx|.x.|xxx|+---+---+---+|xxx|...|xxx||xxx|...|xxx||xxx|...|xxx|+---+---+---+`
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: Symmetric 18s

Hi, coloin!
coloin wrote:Ive just had a look at this pattern .....and it doesnt appear to have valid puzzles
Code: Select all
`+---+---+---+|xxx|xxx|xxx||...|.x.|...||...|.x.|...|+---+---+---+|xxx|.x.|xxx||xxx|.x.|xxx||xxx|.x.|xxx|+---+---+---+|xxx|.x.|xxx||xxx|.x.|xxx||xxx|.x.|xxx|+---+---+---+ `

It's very likely that this pattern has no valid puzzles, but right now I cannot check it because yesterday I encountered a problem in my searching program. I think I need several days to fix that problem. Then I'll check this pattern.

Serg
Serg
2018 Supporter

Posts: 627
Joined: 01 June 2010
Location: Russia

### Re: Symmetric 18s

Hi, remind me again how you check a pattern ?

if a pattern is a potential puzzle
if all the empty spaces in a potential puzzle are pattern-i
Do you ?
generate all possible ED ways to fill the empty clue pattern [pattern-i]
generate a token grid completion for the pattern-i
show that each token pattern generated has > 1 sol ?

C
coloin

Posts: 1749
Joined: 05 May 2005

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