The hardest sudokus (new thread)

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

Re: The hardest sudokus (new thread)

Postby mith » Sun Mar 13, 2022 2:57 pm

Denis, the original discussion for this took place on discord, with a follow-up by rangsk (David Clamage) as part of our youtube discussion series here: https://youtu.be/V7RC1hJ8vZ8

I am working on more formal write-ups for this, my hard-puzzle search, and some other topics (such as the minimal anti-knight search), will link as I have drafts available.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Mar 14, 2022 6:28 am

mith wrote:Denis, the original discussion for this took place on discord, with a follow-up by rangsk (David Clamage) as part of our youtube discussion series here: https://youtu.be/V7RC1hJ8vZ8
I am working on more formal write-ups for this, my hard-puzzle search, and some other topics (such as the minimal anti-knight search), will link as I have drafts available.

Hi mith
Thanks for the reference. I watched the 1st 5 mins yesterday evening, but it's so slow and boring that I literally fell asleep on it.
I'm surprised that he chose such a trivial example: a puzzle with SER = 7.3, solvable in BC3.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Mar 14, 2022 9:25 am

eleven wrote:
Code: Select all
-----------------
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
-----------------
| x . . | . . x |
| . x . | . x . |
| . . x | x . . |
-----------------

For this pattern i showed here, that the 3 digits only are not possible.
This means, that if a puzzle has a solution, at least one other digit in these cells must be true (= the 3 digits must be false in at least one of the cells), wherever one is possible in a given candidates grid.


But this pattern covers only 1 case in 3.
As I proved here: http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html, the pattern in the 4th block may be any of the following and they are not equivalent:
Code: Select all
+-------+
! . . * !
! . * . !
! * . . !
+-------+

+-------+
! . * . !
! * . . !
! . . * !
+-------+

+-------+
! * . . !
! . . * !
! . * . !
+-------+


I also proved that the other 3 cases allow no conclusion.

Coding the rule in CSP-Rules based on my definition was straightforward (it took me 2 hrs). I haven't tried to do it based on your rectangles, so I can't say which is simpler to code.
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Re: The hardest sudokus (new thread)

Postby 999_Springs » Mon Mar 14, 2022 1:14 pm

denis_berthier wrote:the pattern in the 4th block may be any of the following and they are not equivalent:
the 3 patterns are isomorphic.

starting from this:
Code: Select all
+-------+-------+
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
+-------+-------+
| x . . | . . x |
| . x . | . x . |
| . . x | x . . |
+-------+-------+

swap c1 with c2, swap r1 with r2, swap c4 with c5, swap r4 with r5, get this:
Code: Select all
+-------+-------+
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
+-------+-------+
| x . . | x . . |
| . x . | . . x |
| . . x | . x . |
+-------+-------+

also from the same starting point, swap c2 with c3, swap r2 with r3, swap c5 with c6, swap r5 with r6, get this:
Code: Select all
+-------+-------+
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
+-------+-------+
| x . . | . x . |
| . x . | x . . |
| . . x | . . x |
+-------+-------+
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Mar 14, 2022 2:09 pm

999_Springs wrote:
denis_berthier wrote:the pattern in the 4th block may be any of the following and they are not equivalent:
the 3 patterns are isomorphic.

starting from this:
Code: Select all
+-------+-------+
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
+-------+-------+
| x . . | . . x |
| . x . | . x . |
| . . x | x . . |
+-------+-------+

swap c1 with c2, swap r1 with r2, swap c4 with c5, swap r4 with r5, get this:
Code: Select all
+-------+-------+
| x . . | x . . |
| . x . | . x . |
| . . x | . . x |
+-------+-------+
| x . . | x . . |
| . x . | . . x |
| . . x | . x . |
+-------+-------+


I didn't write the patterns are not isomorphic. I wrote they are not equivalent. You should read the whole conditions for being equivalent. Cell r1c1, the target cell, is fixed.
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Re: The hardest sudokus (new thread)

Postby coloin » Mon Mar 14, 2022 7:18 pm

On page 55 of this thread
There are 6 ways to fill in the 4th box (B5)
3 ways are possible to use the 3 clues
3 ways it is not possible to use all 3 clues the diagonal pattern is equivalent … but not in the context of the other 3 boxes ( B1B2B4)
The 3 ways that are impossible would have the hamner pattern with the handle ( albeit offset in 2 of the 3 cases)
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Re: The hardest sudokus (new thread)

Postby mith » Mon Mar 14, 2022 9:09 pm

Code: Select all
........1.....2.......3..45..1.23....2671.8..73.6.81...8.......2.3.86..761..7....  ED=11.9/1.2/1.2
........1.....2.......3..45..6.......71.8....32..67..8.6..23....837..1..7.281.6..  ED=11.9/1.2/1.2
........1.....2.34....562....1.257...267.18...5.68.1...87......5.2.68..761...7...  ED=11.8/1.2/1.2
........1.....2.34235...6......78.6..8.53....3.72.6....72......65...78..8.3.257.6  ED=11.8/1.2/1.2
........1.....2.34....562....1.25....267.18..75.68.1...8.......5.2.68..761...7...  ED=11.8/1.2/1.2
........1.....2.34....562....7.......61..8...25..67..8.7..25....856..1..6.28.17..  ED=11.8/1.2/1.2
........1.....2.34....562....56..1...627.18..8...257...7.......52..68..76.1..7...  ED=11.8/1.2/1.2
........1.....2.34..2.3156.....564...1.2.43.6.4.31..2.....6......4....5.7.8..5...  ED=11.8/1.2/1.2
........1.......2......3..4..2..56.7.3678.....5.2..8.3.675....2.8.37....5.3.62...  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3678.2...5.2..8...675.....28..7....5.3.62...  ED=11.8/1.2/1.2
........1.......2......3..4..2..56.7.3678.....5.2..8.3.675....228.37....5.3.6....  ED=11.8/1.2/1.2
........1.....2.34....562....56..1...627.18..8...257...7.......52..6...86.1..8...  ED=11.8/1.2/1.2
........1.....2.34..2.3156.....56.1..1.2.43.6.4.3...2.....6......4....5.7.8..5...  ED=11.8/1.2/1.2
........1.....2.......3..45..6.......71.8....32..67..8.6..23....8.7.61..7.281.3..  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3678.....5.2..8...675....2.8..7....5.3.62...  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3678.....5.2..8...675....228..7....5.3.6....  ED=11.8/1.2/1.2
........1.....2.34.23...5....623.....7.8.5...2.8.76.5..87......5.2..76..63...87.5  ED=11.8/1.2/1.2
........1.....2.34.23...5....6.78.5...823....37.6.5....67......5.2..78..83...67.5  ED=11.8/1.2/1.2
........1.....2.34....562....7.25....5867.1..62.8.17...16......2.5.68..787.......  ED=11.8/1.2/1.2
........1.....2.34....562....1.25....267.18..75.68.1...87......5.2.67..861.......  ED=11.8/1.2/1.2
........1.....2.34.23...5....6.78....5823.....7.6.5....67.....25.2..78..83...67.5  ED=11.8/1.2/1.2
........1.....2.34.23...5....6.78....5823.....7.6.5....67.....25....78..83..267.5  ED=11.8/1.2/1.2
........1.......2......3..4..2..56.7.3678.2...5.2..8.3.675.....28.37....5.3.62...  ED=11.8/1.2/1.2
........1.....2.34....562....7.......52.67..816...8....8..25...2.67.18..57.6..1..  ED=11.8/1.2/1.2
........1.....2.34....562....567.1...628.17..7...258...87......52..6...76.1......  ED=11.8/1.2/1.2
........1.....2.34235...6....2.78.6..8.23....7..5.6....26..78..3.8...7.657.......  ED=11.8/1.2/1.2
........1.....2.34235...6......78.6..8.23....7.35.6....26..78..3.8...7.657.......  ED=11.8/1.2/1.2
........1.....2.34....562....1.257...267.18...5.68.1...87......5.2.6...861.......  ED=11.8/1.2/1.2
........1.....2.34.23...5....6.78.5...823.....7.6.5....67.....25....78..83..267..  ED=11.8/1.2/1.2
........1.....2.34.23...5....6.78.5...823.....7.6.5....67.....25.2..78..83...67..  ED=11.8/1.2/1.2
........1.....234...2.315.6....652...2.1.4..3.4.3..15...4...6...6..53...7.8..6...  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...3782.5..86.5..2...786.....52..8....6.3.75...  ED=11.8/1.2/1.2
........1.......2......3..4..5.367.8.3782.5...6.5..2...786.....52..8....6.3.75...  ED=11.8/1.2/1.2
........1.......2......3..4..3.5.2...5.3.67.8.7628.5...87.6....5.28.....63.7.5...  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...3782.5..86.5..2...7.6.....52..8....6.3.75.8.  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...6782.5..83.5..2...786.....52..8....6.3.75...  ED=11.8/1.2/1.2
........1.......2......3..4..5..67...6728.5..83..5.2...78.6....52.83....6.37.5...  ED=11.8/1.2/1.2
........1.......2......3..4..3.5.2...5...67.8.7628.5...87.6....5.283....63.7.5...  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...6782.5..83.5..2...7.6.....52..8....6.3.75.8.  ED=11.8/1.2/1.2
........1.......2......3..4..5..67...6728.5..83..5.2...7..6....52.83....6.37.5.8.  ED=11.8/1.2/1.2

11.7s:
Hidden Text: Show
Code: Select all
........1....23.....2145.....6.....7.1.6...28.782..96...7..26.9.89....126.....78.  ED=11.7/1.2/1.2
........1....23......145.....16...27.78...96.26......8.8...26.9.97....126.2...87.  ED=11.7/1.2/1.2
.......12......345....13.....3..67...6879....17...8....8..79..1.963.....7.168....  ED=11.7/1.2/1.2
........1....23.....2145.....6.....7.1.6...28.782..96...7...6.9.89....1.62....78.  ED=11.7/1.2/1.2
........1....23.....2145.....6..2.78.7....96.9.8...1...27.....61..7..2.96.9...78.  ED=11.7/1.2/1.2
........1....23......145.....16...27.6......8.782..96..8....6.9.97....126.2...87.  ED=11.7/1.2/1.2
........1.....2.34235...6......78.....72.6....8653.....72.....56....78..8.3.257.6  ED=11.7/1.2/1.2
........1.....2.34235...6......78.....72.6....8653.....72.....565...78..8.3.2.7.6  ED=11.7/1.2/1.2
........1.....2.34235...6......78.6...72.6....8.53.....72.....56....78..8.3.257..  ED=11.7/1.2/1.2
........1.....2.34235...6......78.6...72.6....8.53.....72.....565...78..8.3.2.7..  ED=11.7/1.2/1.2
........1.....2.......3..45..6.......23.78..618..6...7.7..23...2.861.7..36.8..1..  ED=11.7/1.2/1.2
........1.......2......3..4..2.356.7.3.2..8...5678.2...675.....28..7....5.3.62...  ED=11.7/1.2/1.2
........1.......2......3..4..2..56.7.3..2.8...5687.2...67.5....28.73....5.36.2...  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...6782.5.38..5..2...786.....52..8....6.3.75...  ED=11.7/1.2/1.2
........1.......2......3..4..2.356.7.3.2..8...5678...3.675.....28..7....5.3.62...  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3678....75.2..8.3.675....2.8.37....5.3.62...  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3678....75.2..8.3.675....228.37....5.3.6....  ED=11.7/1.2/1.2
........1....23....24....35....46.....67..8...4283...7.3..8.....682.4.7.4.7.6....  ED=11.7/1.2/1.2
........1.......2......3..4..2..56.7.3..2.8...5687.....67.5...2.8.73....5.36.2...  ED=11.7/1.2/1.2
........1.......2......3..4..2.356.7.3.2..8...5678.....675....2.8..7....5.3.62...  ED=11.7/1.2/1.2
........1.......2......3..4..2..56.7.3..2.8...5687.....67.5...228.73....5.36.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.356.7.3.2..8...5678.....675....228..7....5.3.6....  ED=11.7/1.2/1.2
........1.....2.34..2.3156.....564...1.2.4..6.4.3...2.....6......4....5.7.81....3  ED=11.7/1.2/1.2
........1.....2.34..2.3.56.....564...1.2.4..6.4.31..2.....6......4....5.7.81....3  ED=11.7/1.2/1.2
........1.....2.34..2.3156.....56.1..1.2.4..6.4.3...2.....6......4....5.7.81....3  ED=11.7/1.2/1.2
........1.....2.....2.3..45..671.3...7.6.81...8..23....23.86..716..7....8........  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3678.2..75.2..8.3.675.....28.37....5.3.62...  ED=11.7/1.2/1.2
........1.......2......3..4..5..67...3728.5...6..5.2.3.78.6....52.83....6.37.5.8.  ED=11.7/1.2/1.2
........1.......2......3..4..5..67...3728.5..86..5.2.3.78.6....52.83....6.37.5...  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...3782.5...6.5..2.3.786.....52..8....6.3.75.8.  ED=11.7/1.2/1.2
........1.......2......3..4.25.367..3.782.5..68.5....3.63.75...25..8....7.86.....  ED=11.7/1.2/1.2
........1.......2......3..4..5.6...3.7328.6..26.3.57...87.5....53.7.6.8.6.28.....  ED=11.7/1.2/1.2
........1.......2......3..4..5.6...3.7328.6..26...57...87.5....53.7.6.8.6.283....  ED=11.7/1.2/1.2
........1.......2......3..4.25..67..3.728.5..68..5...3.637.5...25.83....7.8.6....  ED=11.7/1.2/1.2
........1......234....14.5...4.56.....718.....6...7.8..85.4....47.6....56.157...8  ED=11.7/1.2/1.2
........1......234....14.5...61......7.4.6.8.8.4.57....85......46.7.8..57.156....  ED=11.7/1.2/1.2
........1......234....14.5...6..7.8..7.1.....84..56....58.4....4.76.8..561.57....  ED=11.7/1.2/1.2
........1......234....14.5...5.......6157...874.6.8..5..71......84.56...6..4.7.8.  ED=11.7/1.2/1.2
........1......234....14.5...5.4.....6157...874.6.8..5..71......84.56...6....7.8.  ED=11.7/1.2/1.2
........1......234....14.5...4.56.....718.....6.4.7.8..85......47.6.8..56.157....  ED=11.7/1.2/1.2
........1......234....14.5...4.56.....718.....6.4.7.8..85......47.6....56.157...8  ED=11.7/1.2/1.2
........1......234....14.5...4.56.....718.....6...7.8..85.4....47.6.8..56.157....  ED=11.7/1.2/1.2
........1...234.....2.15.....67..89..78...1.292......6.1....7...67.9..288.9...6..  ED=11.7/1.2/1.2
........1....23.....4.56.....7.....4..85..79.19.7..5.8.41.7.8.9.8.....4.5.9...17.  ED=11.7/1.2/1.2
........1....23.....4.56.....75..89..5......418.9...57.41....785.8...91.97....4..  ED=11.7/1.2/1.2
........1....23.....4.56.....7.....4..85..79.19.7..5.8.41...8.95.9...17.78.....4.  ED=11.7/1.2/1.2
........1.......2......3..4..5.367.8.3782.5...6.5....3.786.....52..8....6.3.75...  ED=11.7/1.2/1.2
........1.......2......3..4..5..67.8.3728.5...6..5...3.78.6....52.83....6.37.5...  ED=11.7/1.2/1.2
..............1.23....45..6..2.1...7.63....817.....26..27......38....71.6.18...32  ED=11.7/1.2/1.2
........1.......2......3..4..5..67...3728.5..86..5...3.7..6....52.83....6.37.5.8.  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...3782.5..86.5....3.7.6.....52..8....6.3.75.8.  ED=11.7/1.2/1.2
........1.......2......3..4..2..56.7.3..2.8...5687...3.67.5....28.73....5.36.2...  ED=11.7/1.2/1.2
..............1.23....45..6..1.547...7586....84........6841....4....8.6.51..76...  ED=11.7/1.2/1.2
..............1.23....45..6..2.1...7.63....817.....26..271.....38....7..6.18...32  ED=11.7/1.2/1.2
..............1.23....45..6..1.547...7586....84....6...6841....4....8...51..76...  ED=11.7/1.2/1.2
..............1.23....45..6..2.....7.63....8171....26..271.....38....7..6.18...32  ED=11.7/1.2/1.2
........1.....2.34..3...5.6..2.78....375.....68..3..5..7..2....2.8..76..35.86....  ED=11.7/1.2/1.2
........1.....2.34.23...5.6..2.78....375.....68..3..5...8..76...7..2....35.86....  ED=11.7/1.2/1.2
........1.....2.34..3...5.6..2.78....375.6....8..3..5..76.2....2.8..76..35.8.....  ED=11.7/1.2/1.2
........1.....2.34.23...5.6..2.78....375.6....8..3..5...8..76...76.2....35.8.....  ED=11.7/1.2/1.2
........1.....2.34..3...5.6..2.78....375.....68.23..5..7.......2.8..76..35.86....  ED=11.7/1.2/1.2
........1.....2.34.23...5.6....78....375.....68.23..5..7.......2.8..76..35.86....  ED=11.7/1.2/1.2
........1.....2.34..3...5.6..2.78....375.6....8.23..5..76......2.8..76..35.8.....  ED=11.7/1.2/1.2
........1.....2.34.23...5.6....78....375.6....8.23..5..76......2.8..76..35.8.....  ED=11.7/1.2/1.2
........1.....2.3...4...2.5..6.47.8..4.6.....78.32.....2.78.3...67..48..3..2.6...  ED=11.7/1.2/1.2
........1.....2.34.23...5....2.67.8..365.....87..3..5...7..68...6..2....35.78....  ED=11.7/1.2/1.2
........1.....2.3...4...2.5..6.47.8..4.6.8...7..32.....2.7..3...67..48..3.82.6...  ED=11.7/1.2/1.2
........1.....2.34.23...5....2.67.8..365.8....7..3..5...7..68...68.2....35.7.....  ED=11.7/1.2/1.2
........1.....2.3...4...2.5....6......64.7.8.78.23.....67..48..3...26...42.87.3..  ED=11.7/1.2/1.2
........1.....2.34.23...5......67.8..365.....87.23..5..6.......2.7..68..35.78....  ED=11.7/1.2/1.2
........1.....2.3...4...2.5....67.....64.8.7..8.23.....37.26...24..8.3..6.8..47..  ED=11.7/1.2/1.2
........1.....2.34.23...5......67.8..365.8....7.23..5..68......2.7..68..35.7.....  ED=11.7/1.2/1.2
........1.....2.34..2.3.56.....56.1..1.2.4..6.4.31..2.....6......4....5.7.81....3  ED=11.7/1.2/1.2
........1......234.....5.......67.....62.8.79.2759...8.79.52...2.86.....65.87.9..  ED=11.7/1.2/1.2
........1...234.....2..5..........67..6.782.9..7..918..29...6..16.8..97.7.8....12  ED=11.7/1.2/1.2
..............1..2....34.56.17......34..18.9.9.8.......7184.9..49.1.37..8.3.79...  ED=11.7/1.2/1.2
........1..2..3....41.56..........27......8.9.29.8.41..78...9.42.47...8.91.8...72  ED=11.7/1.2/1.2
........1.....2..3....45.67.152.48..28.95....4.9.81....54.29.1.82.......9.1......  ED=11.7/1.2/1.2
........1.....2..3....45.67..8.......29.1....45..28.1..9285....51.2.49..8.4.91...  ED=11.7/1.2/1.2
........1......234....25.......67.....6..8.79.2759...8.79.52...2.86.....65.87.9..  ED=11.7/1.2/1.2
........1......234....25.......67.....6..8.79.2759...8.79.52...2.86.9...65.87....  ED=11.7/1.2/1.2
........1......234....25.......67.....62.8..9.2759..8..79.52...2.86.9...65.87....  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....4.827.6..756.8...46.27...25.6.8...7.8......  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....4.827.6..756.8...46..7...25.6.8...7.8.5....  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....4.827.6..756.8...46..7...25...8...7.8.5..6.  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....5.827.6.7.56.8...87......46..27...5.26.8...  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....4.827.6..756.8...46.27...25...8...7.8....6.  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....5.827.6.7.56.8...87....6.46..27...5.2..8...  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8695....79.4.8....47.9....65..8....8.96.75..  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8695....79...8....47.9....65..84...8.96.75..  ED=11.7/1.2/1.2
........1.......23....45..6..4..7....85..96..79.68.4...5..68....679.4...8.957....  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8.95....79.4.8.6..47.9....65..8....8.96.75..  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8.95....79...8.6..47.9....65..84...8.96.75..  ED=11.7/1.2/1.2
........1.......23....45..6..4.57....85..96..79.68.4...5..68....679.4...8.9.7....  ED=11.7/1.2/1.2
........1.......23....45..6..4..7....856.94..79..8.6...5..68....679.4...8.957....  ED=11.7/1.2/1.2
........1.......23....45..6..4.57....856.94..79..8.6...5..68....679.4...8.9.7....  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8695....79.4.8....47.9.5..65..8....8.9..76..  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8695....79...8....47.9.5..65..84...8.9..76..  ED=11.7/1.2/1.2
........1.......23....45..6..4.7.....8695....79.4.8.6..4769.5..65..8....8.9..7...  ED=11.7/1.2/1.2
........1.......23....45..6..4.7.....8695....79...8.6..4769.5..65..84...8.9..7...  ED=11.7/1.2/1.2
........1.......23....45..6..4.7.....8695....79...8.6..47.9....65..84...8.96.75..  ED=11.7/1.2/1.2
........1.......23....45..6..4.7.....8695....79.4.8.6..47.9....65..8....8.96.75..  ED=11.7/1.2/1.2
........1.......23....45.....4.67....8.95....69...8.7..46.9.7..75..84...8.97.65..  ED=11.7/1.2/1.2
........1.......23....45.....4.67....8.95....69.4.8.7..46.9.7..75..8....8.97.65..  ED=11.7/1.2/1.2
........1......234.....5........6.....657..89..82.9.67.298.....58.96.7..6.7.52...  ED=11.7/1.2/1.2
........1......234.....5........6.....657..89..82.9.67.298.7...58.96....6.7.52...  ED=11.7/1.2/1.2
........1..2.34....56.17..........38......9.4.9..4371......84.78..37..9.9....1.83  ED=11.7/1.2/1.2
..............1.23....45.67.26....8.8.39...7.97.8..3.6.92......3.8......76..9..32  ED=11.7/1.2/1.2
..............1..2....34.56..7.......18.9....34..17.9..8174.9..49.1.38..7.3.8....  ED=11.7/1.2/1.2
..............1.23....45.67..2.......38....9.67..9..32.839...7.2.6....8.79.8..3.6  ED=11.7/1.2/1.2
........1.....2..3....4..56..7.......89..1...24..78.1..987.4...41.82.9..7.2.19...  ED=11.7/1.2/1.2
........1......234....25........6.....657..89..8..9.67.298.....58.96.7..6.7.52...  ED=11.7/1.2/1.2
........1......234....25........6.....657..89..8..9.67.298.7...58.96....6.7.52...  ED=11.7/1.2/1.2
..............1..2....3..45..6.......78..9...13..67.9..876.39..39.71.8..6.1.98...  ED=11.7/1.2/1.2
........1....23.....4.56.....7....5...87..9.419.5...87.41.8..795.9...81.8.....4..  ED=11.7/1.2/1.2
........1......234....25........6.....657..89..92.8..7.289.7...59.86....6.7.52...  ED=11.7/1.2/1.2
........1.....2..3....45.67..5.......89..1...24..58.1..98..4...41.82.9..5.2.19...  ED=11.7/1.2/1.2
..............1..2....34.56..4.......78..9...13..47.9..87..39..39.71.8..4.1.98...  ED=11.7/1.2/1.2
..............1..2....34.56.13.47.8.48.......9.7.......3871.9..14..89...7.9..38..  ED=11.7/1.2/1.2
........1.....2..3....45.67.1482.9..2.5.19...89...4....42.58.1.5.1......98.......  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...6782.5.38..5..2...7.6.....52..8....6.3.75.8.  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....5.827.6.7..6.8...87.5....46...7...5.26.8...  ED=11.7/1.2/1.2
........1.......23...2456.....7.4.....5.827.6.7..6.8...87.5..6.46...7...5.2..8...  ED=11.7/1.2/1.2
........1....23.....2145..........67.8...219.9.7...2.8.18.....2.7.6...896.9...7..  ED=11.7/1.2/1.2
........1.......23....45..6..7..8....8579..6.69..5.....46.8....5.9.674..87...9...  ED=11.7/1.2/1.2
........1.......23....45..6..76.8....8579....69..5.....46.8....5.9.674..87...9...  ED=11.7/1.2/1.2
........1.....2.34.25........2.6....6.785.9..89...7....6892.....7.5.8.6.5.9.7....  ED=11.7/1.2/1.2
........1.....2345.23........2.6....6.783.9..89...7....6892.....7...8.6.3.9.7....  ED=11.7/1.2/1.2
........1....23.....4..5.....6.78.9..1......698....4.7.498...1.16.7..8.97......64  ED=11.7/1.2/1.2
........1......234....25.....627.....75.89...8..5.6.9..8296.7..65.8.....7.9......  ED=11.7/1.2/1.2
........1......234....25.....6.......7268.9..85.7.9.....829.....95.76...7..5.8.6.  ED=11.7/1.2/1.2
........1..2..3.....1.45..........67..7.8619..9....2.8.86....722.96.....71.8....9  ED=11.7/1.2/1.2
........1....23.45.251..36.........6.7.4......896..........51.42..34....5...16.23  ED=11.7/1.2/1.2
........1....2345...24.1.36.....6..4...31..2.12..453.....65.....7....6..89....5..  ED=11.7/1.2/1.2
........1..2..3.....1.45.....6.78.9..1......698....2.7.298...1..6.7..8.97......62  ED=11.7/1.2/1.2
........1..2..3.....1.45..........67..7.8.19.69....2.8.8.....722.96.....71.8..6.9  ED=11.7/1.2/1.2
........1..2..3.....1.45..........67..7.8.19.69....2.8.86....722.96.....71.8....9  ED=11.7/1.2/1.2
........1..2..3.....1.45.....6.7..8..1.....9689....2.7.289...1..6.7..9.87......62  ED=11.7/1.2/1.2
........1....2345...24.1.36.....6..4...31..2512..453.....65.....7....6..89.......  ED=11.7/1.2/1.2
........1.....2.34.25..........67...6.895.7..9..2.8....69......28.5.9.675.7.8....  ED=11.7/1.2/1.2
........1.....2.34.25........2.67...6.895.7..9....8....69.2.....8.5.9.675.7.8....  ED=11.7/1.2/1.2
........1.....2.34.25..........6....6.785.9..89.2.7....689.....27.5.8.695...7....  ED=11.7/1.2/1.2
........1.....2.34.25........2.6....6.785.9..89...7....6892.....7.5.8.695...7....  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7819..1.....869.....4.7.498.....16.7....97.8....64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7819..1......698....4.7.498.....16.7..8.97......64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.78.9..1.....869.....4.7.498...1.16.7....97.8....64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7.18..1.....9689....4.7.489.....16.7..9.87......64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7.18..1.....9689....4.7.489.....16.7....87.9....64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7..8..1.....9689....4.7.489...1.16.7..9.87......64  ED=11.7/1.2/1.2
........1....23.....4..5.....6.7..8..1.....9689....4.7.489...1.16.7....87.9....64  ED=11.7/1.2/1.2
........1.....2.34.25..........67...6.895.7..9..2.8....697.....28.5.9.6.5.7.8....  ED=11.7/1.2/1.2
........1.....2.34.25........2.67...6.895.7..9....8....6972.....8.5.9.6.5.7.8....  ED=11.7/1.2/1.2
........1.....2.34.25..........6....6.785.9..89.2.7....689.....27.5.8.6.5.9.7....  ED=11.7/1.2/1.2
........1....2345...24.1.36.....6..4...31..2.12..453......5.....7....6..896...5..  ED=11.7/1.2/1.2
........1....2345...24.1.36.....6..4...31..2512..453......5.....7....6..896......  ED=11.7/1.2/1.2
........1.....2345.23..........67...6.893.7..9..2.8....69......28...9.673.7.8....  ED=11.7/1.2/1.2
........1.....2345.23........2.67...6.893.7..9....8....69.2.....8...9.673.7.8....  ED=11.7/1.2/1.2
........1.....2345.23..........6....6.783.9..89.2.7....689.....27...8.693...7....  ED=11.7/1.2/1.2
........1.....2345.23........2.6....6.783.9..89...7....6892.....7...8.693...7....  ED=11.7/1.2/1.2
........1......234....25.....6.......7268.9..85.7.9.....82......95.76...7..5.8.69  ED=11.7/1.2/1.2
........1....2345...24.1.36....5.....7....6..896...5.....2.6..4...31..2.1...453..  ED=11.7/1.2/1.2
........1....2345...24.1.36....5.....7....6..896.........2.6..4...31..251...453..  ED=11.7/1.2/1.2
........1.....2345.23..........67...6.893.7..9..2.8....697.....28...9.6.3.7.8....  ED=11.7/1.2/1.2
........1.....2345.23........2.67...6.893.7..9....8....6972.....8...9.6.3.7.8....  ED=11.7/1.2/1.2
........1.....2345.23..........6....6.783.9..89.2.7....689.....27...8.6.3.9.7....  ED=11.7/1.2/1.2
........1...234.....2.15.....6.....7.87.6.29.91......8..87..6.9.79....1.62.....8.  ED=11.7/1.2/1.2
........1....23.....4.56.....7.....4..87..59.19.5....8.59...17..8.....4.4.1.7.8.9  ED=11.7/1.2/1.2
........1....23.....4.56.....7.....4..87..59.19.5....8.59...17.4.1...8.978.....4.  ED=11.7/1.2/1.2
........1....23.....4.15.....6.....7.87.6.49.91......8..87..6.9.79....1464.....8.  ED=11.7/1.2/1.2
........1.......23....45.....4.56....75..89..68.97.4...5...7....968.4...7.8.6..9.  ED=11.7/1.2/1.2
........1.......23....45.....4..6....75..89..68.97.4...5...7....968.4...7.856..9.  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8.95....79...8.6..47.9.5..65..84...8.9..7...  ED=11.7/1.2/1.2
........1.......23....45.....4..6....758.94..69..7.8...5...7....869.4...7.956..8.  ED=11.7/1.2/1.2
........1.......23....45.....4.56....758.94..69..7.8...5...7....869.4...7.9.6..8.  ED=11.7/1.2/1.2
........1.......23....45..6..4.76....8.95....79.4.8.6..47.9.5..65..8....8.9..7...  ED=11.7/1.2/1.2
........1.......23....45.....4.67....8.95....69.4.8.7..46.9.5..75..8....8.9..67..  ED=11.7/1.2/1.2
........1.......23....45.....4.67....8.95....69...8.7..46.9.5..75..84...8.9..67..  ED=11.7/1.2/1.2
........1....23.....4.56..........5...78..9.419.5...78.41.7..89.8....4..5.9...71.  ED=11.7/1.2/1.2
........1.....2.34....56.....7.......285.17..65..8.1...167.5...2.5.68..78..2.....  ED=11.7/1.2/1.2
........1.......23....45..6..6..7....48.9.5..97..8.6...5967....7..9.8...8...54...  ED=11.7/1.2/1.2
........1....23.....2145..........67.8....19.9.7...2.8.18.......7.6...896.92..7..  ED=11.7/1.2/1.2
........1.......23....45..6..7..4.....89.7..5.9.68.....65..8...47..9.5..8.9.7.6..  ED=11.7/1.2/1.2
........1.......23....45..6..7..4....489.7....9.68.....65..8...47..9.5..8.9.7.6..  ED=11.7/1.2/1.2
........1.......23....45..6..7..4....489.7.6..9.68.....65..8...47..9.5..8.9.7....  ED=11.7/1.2/1.2
........1.......23....45.....6..4....478.6.9..8.97.....95..7...46..8.5..7.8.6.9..  ED=11.7/1.2/1.2
........1.......23....45..6..7..4....8.69.....948.7....65..9...47..8.5..9.8.7.6..  ED=11.7/1.2/1.2
........1.......23....45..6..4.7.....78..96..95..684...69.5....5.789....8....7...  ED=11.7/1.2/1.2
........1.......23....45.....4.6.....67..89..85..974...98.5....5.678..9.7....6...  ED=11.7/1.2/1.2
Last edited by mith on Mon Mar 14, 2022 9:32 pm, edited 2 times in total.
mith
 
Posts: 996
Joined: 14 July 2020

Re: The hardest sudokus (new thread)

Postby mith » Mon Mar 14, 2022 9:10 pm

And the 11.6s split because the hidden tag doesn't play nicely with such a long list:
Hidden Text: Show
Code: Select all
..............1.23.....24.5.12.67...68.92..7.7.91.8.6..97......16..8....2.8..96.7  ED=11.6/1.2/1.2
..............1.23.....24.5.12.67...68.92..7.7.91.8.6..97..6...16..8....2.8..9..7  ED=11.6/1.2/1.2
........1.....2.34.....35.6.12.7....7.3..81.998........7183..9.32..19...8.92.7...  ED=11.6/1.2/1.2
........1.....2.34.....35.6.12.7....7.3..8..998........7183..9.32..19...8.92.7.1.  ED=11.6/1.2/1.2
........1....23.....4..5.....6.78.9..1.....869.....4.7.497..86.16.8..7.97.8....14  ED=11.6/1.2/1.2
........1....23.....4..5.....6.7819..1.....869.....4.7.497..86.16.8..7.97.8.....4  ED=11.6/1.2/1.2
........1....23.....41.5.....6.78.9..1.....869.....4.7.497..86.16.8..7.97.8.....4  ED=11.6/1.2/1.2
........1.....2.34.25........6.27....528.9...87.56.9...68......2.7.56.8959.7.....  ED=11.6/1.2/1.2
........1.....2.34.25....6...7.28....529.....98.57.6...79.6....2.8.57.9.56.8.....  ED=11.6/1.2/1.2
........1.....2.34.25........6.27....528.9...87.56.9...68.9....2.7.56.8.59.7.....  ED=11.6/1.2/1.2
........1.....2.34.25.......52.6....67.85.9..9.82.7....869.....2.75.8.6.59..7....  ED=11.6/1.2/1.2
..............1.23.....24.5..6.......1789....82...67.9.7826..9.2.17.....69..18.7.  ED=11.6/1.2/1.2
..............1.23.....24.5.12.6....67.82..9.9.81.7.6..89......16.97....2.7..86..  ED=11.6/1.2/1.2
..............1.23.....24.5..6..7....1789....82...6..9.7826..9.2.17.....69..18.7.  ED=11.6/1.2/1.2
........1.....2345.23.......32.6....67.83.9..9.82.7....869.....2.7..8.6.39..7....  ED=11.6/1.2/1.2
........1.....2345.23........6.27....328.9...87.36.9...68.9....2.7..6.8.39.7.....  ED=11.6/1.2/1.2
........1.....2345.23....6...7.28....329.....98.37.6...79.6....2.8..7.9.36.8.....  ED=11.6/1.2/1.2
........1..2..3.....1245..........67..7.6819..9....2.8.68....121.9....7.72.8..6.9  ED=11.6/1.2/1.2
........1.....2345.23........6.27....328.9...87.36.9...68......2.7..6.8939.7.....  ED=11.6/1.2/1.2
.......12.....3..4..5...3.6..7.8..49.3..97...8..5.4....5897....37.4.89..4.9..5...  ED=11.6/1.2/1.2
........1..2..3.....1245.....6.7.18..8....2.99......76.79....121.8....6.62.9..7.8  ED=11.6/1.2/1.2
........1..2..3.....1245.....6.7.18..8....2.99......76.7.....121.8...96.62.9..7.8  ED=11.6/1.2/1.2
........1.....2.34.....35.6..7.......2189....83...71.9.1837..9.3.21.....79..28...  ED=11.6/1.2/1.2
........1.....2.34.....35.6.1278....7.3..91..89........7139..8.32.1.....9.8.27...  ED=11.6/1.2/1.2
........1.....2.34.....35.6..7.......2189....83...7..9.1837..9.3.21.....79..28.1.  ED=11.6/1.2/1.2
........1......234....25.6...5.78.....92.6....8..9..76.67.52...59.68....8.27.9...  ED=11.6/1.2/1.2
........1..2..3.....1.45..........67..7.8619..9....2.8.86.....22.98..67.71.6..8.9  ED=11.6/1.2/1.2
........1.....2345.23........2.67...78...96..9..83.....687.....27...6.9.3.9.28...  ED=11.6/1.2/1.2
........1....23......145.....6....17.18...92.79.2..8.6.67.8....1.9.6..7.82.....9.  ED=11.6/1.2/1.2
........1....23.....1.45.....6....17.18...94.79.4..8.6..9.6..78.4.....9..67.8.1..  ED=11.6/1.2/1.2
........1....23.....1.45.....6....17.18...94.79.4..8.6..9.6..7..67.8.1..84.....9.  ED=11.6/1.2/1.2
...............123.....1.45..1.67..8.9..5....87...9..6.59.18...6.879.5..71...6...  ED=11.6/1.2/1.2
...............123.....1.45..1.67..8.7...9..6.9.85.....59.18...6.879.5..71...6...  ED=11.6/1.2/1.2
...............123.....1.45..1.67..8.9..5....87.1.9..6.59..8...6.879.5..71...6...  ED=11.6/1.2/1.2
...............123.....1.45..1.67..8.7.1.9..6.9.85.....59..8...6.879.5..71...6...  ED=11.6/1.2/1.2
........1......234.....2.5...2.67....8.95....97.2.8.6..58..9...6.978.5..72...6...  ED=11.6/1.2/1.2
........1......234.....2.5...2.67....8.95....97...8.6..58.29...6.978.5..72...6...  ED=11.6/1.2/1.2
........1......234.....2.5...6.27....2891....79.8.61...67......2.9.78..681..9....  ED=11.6/1.2/1.2
........1....23.....41.5.....6.7..84.7....9.69.8...17..897..64.14....7.96.......8  ED=11.6/1.2/1.2
........1....23......145.....2....6..78.9....16..8..79.8.....17.91...62.7.62..9.8  ED=11.6/1.2/1.2
........1....23.....41.5.....6.78.9..1......698....4.7.497..86.16.8..7.97.......4  ED=11.6/1.2/1.2
........1....23.....41.5.....6.7..8..1.....9689....4.7.487..96.16.9..7.87.......4  ED=11.6/1.2/1.2
........1....23.....4..5.....6.7819..1......698....4.7.497..86.16.8..7.97.......4  ED=11.6/1.2/1.2
........1....23.....4..5.....6.7.18..1.....9689....4.7.487..96.16.9..7.87.......4  ED=11.6/1.2/1.2
........1..2..3.....1.45..........67..7.8.19.69....2.8.8......22.98..67.71.6..8.9  ED=11.6/1.2/1.2
........1.....2.34.25........6..7....52.89...87.65.9....75.6.89.68.2....59..7....  ED=11.6/1.2/1.2
........1.....2.34.25....6...7..8....52.9....98.75.6....85.7.9..7962....56..8....  ED=11.6/1.2/1.2
........1.....2.34.25........6..7....52.89...87.65.9....75.6.8..6892....59..7....  ED=11.6/1.2/1.2
........1.....2.34.25........6.57.8..7829....59.6......528.....86.57.9..9.7..6...  ED=11.6/1.2/1.2
........1....23.....4..5.....6.78.9..1......698....4.7.497..86.16.8..7.97......14  ED=11.6/1.2/1.2
........1....23.....4..5.....6.7..8..1.....9689....4.7.487..96.16.9..7.87......14  ED=11.6/1.2/1.2
........1....23.45.251..36......5..4...34.12.2...16.53.5......6.7.4......896.....  ED=11.6/1.2/1.2
........1...234.....2..5.....6.78.9..1.....76.9....2.8.78....121.9....6.62.8..7.9  ED=11.6/1.2/1.2
........1.....2345.23........6..7....32.89...87.63.9....7..6.89.68.2....39..7....  ED=11.6/1.2/1.2
........1......234....25.....5.67.....82.9....7..8..69.96.52...58..7....7.26.89..  ED=11.6/1.2/1.2
.......12.....3..4..5...3.6..7.8..49.3...7...89.5.4....5897....37.4.89..4....5...  ED=11.6/1.2/1.2
.......12.....3..4..5...3.6..7.8..4..3..97...89.5.4....5897....37.4.89..4....5...  ED=11.6/1.2/1.2
........1.....2345.23....6...7..8....32.9....98.73.6....8..7.9..7962....36..8....  ED=11.6/1.2/1.2
........1......234....25.6...7.52....827.96..95..8......92.6....65.78...8...9..7.  ED=11.6/1.2/1.2
........1..2..3.....1245.....6....7..89....1272.9..8.6..7.8..6..6....2.991.....87  ED=11.6/1.2/1.2
........1..2..3.....1245.....6...78..9.....1282.7..9.6..8.9..6..6....2.771.....98  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7..8..8....2.991.....76.79....121.8....6.62.9..7.8  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7..8..8....2.991.....76.7.....121.8...96.62.9..7.8  ED=11.6/1.2/1.2
........1.....2345.23........6..7....32.89...87.63.9....7..6.8..6892....39..7....  ED=11.6/1.2/1.2
........1.....2345.23........6..7.8..7829....39.6......328.....86.37.9..9.7..6...  ED=11.6/1.2/1.2
........1......234....25.....6.7..8..7.2.9...95..86....89.52...5.7.6....62.8.79..  ED=11.6/1.2/1.2
........1......234....25.....6.52....726.89..85.97......82.9....95.67...7...8..6.  ED=11.6/1.2/1.2
........1....23.45.251..36.........6.7.4......896..........5..42...16.535..34.12.  ED=11.6/1.2/1.2
........1......234....25.....6.78....8.5.6.9.57.29.....956.78..2.79.....86.......  ED=11.6/1.2/1.2
........1.....2345.23..........67...78.2.96..9..83.....687.....27...6.9.3.9..8...  ED=11.6/1.2/1.2
........1....23.....41.5..........67..7.8.9.4.69...81..78.....941......69.68..47.  ED=11.6/1.2/1.2
........1....23.....1.45.....6....17..8...94.79.4..8.6.4.....9..67.8....1.9.6..78  ED=11.6/1.2/1.2
........1....23.....1.45.....6....17..8...94.79.4..8.6.67.8....1.9.6..7.84.....9.  ED=11.6/1.2/1.2
........1......234.....2.....2.56..7.7.89....86.2...5..97..8...5.867.9..62...5...  ED=11.6/1.2/1.2
........1......234.....2.....2.56..7.7.89....86.....5..97.28...5.867.9..62...5...  ED=11.6/1.2/1.2
........1....23.....1..4....1...5.675.....89.7.8.6.....869..75.1.7.....695.....18  ED=11.6/1.2/1.2
...............123.....1..4..1.56.7..86.9....57......9.956.78..61.98....7...15...  ED=11.6/1.2/1.2
........1....23.....1..4........5.67.5....89..78.6.1...17.....659......88.69..75.  ED=11.6/1.2/1.2
........1.....2345.23........6..7.8..7829....39.6.8....328.9....6.37....9.7..68..  ED=11.6/1.2/1.2
........1.....2345.23........6..7.8..7.29....39.6.8....328.9...86.37....9.7..68..  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....564...1.2.43...4.31..26..4....5..5..63...7.8..5...  ED=11.6/1.2/1.2
........1.....2.3.....45..6..1.24....457.18..72.58.1...8.......4.2.58..751...7...  ED=11.6/1.2/1.2
........1.....2.3.....45..6..1.24....257.18..74.58.1...8.......4.2.58..751...7...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....564...1.2.43...4.31..26..4....5...7.63...8....5...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....564...1.2.43.6.4.31..2...4....5...7.63...8....5...  ED=11.6/1.2/1.2
........1.....2.....3...245....36.....67.8.9..3892..67..7.6.....698.37..82...9...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56.1..1.2.43...4.3...26..4....5..5..63...7.8..5...  ED=11.6/1.2/1.2
........1.....2.34....5627...1.25.....67.18...7.68.1...52.68..716...7...8........  ED=11.6/1.2/1.2
........1.....2.....3...245....36.....67.8.9..3892..67..7.6.....698.3...82..79...  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....56....1.2.43.5.4.31..26..4.......5..63...7.81.5...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56....1.2.43.5.4.3...26..4.......5..63...7.81.5...  ED=11.6/1.2/1.2
........1.....2.34235...6......78...68.23....7..5.6....26..78..3.8...7.657......2  ED=11.6/1.2/1.2
........1.....123...1.245.6..3...6...6..52...7.8..6....1..654...3.2...5..4.1.3..2  ED=11.6/1.2/1.2
........1.....2.34....5627...1.25.....67.18...7.68.1...52.68...16...7...8.7......  ED=11.6/1.2/1.2
........1.....2.34235...6......78...68.23....7..5.6.....6..78..3.8.2.7.657......2  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56....1.2.43.6.4.31..2.....63.....4....5.7.8..5...  ED=11.6/1.2/1.2
........1.....2.3.....45..6..7.......51..8...24..57..8.7..24....825..1..5.48.17..  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56.1..1.2.43.6.4.3...2...4....5...7.63...8....5...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56.1..1.2.43...4.3...26..4....5...7.63...8....5...  ED=11.6/1.2/1.2
........1.....2.3.....45..6..7.......51..8...24..57..8.7..24....845..1..5.28.17..  ED=11.6/1.2/1.2
........1.....2.34.35...6....7.5....3.8..6...52.8.7.6..82......6...387..7..2.5..6  ED=11.6/1.2/1.2
........1.....2.34.35...6....7.5.....2.8.7.6.3.8..6....82......65..387..7..2.5..6  ED=11.6/1.2/1.2
........1.....2.34....5627...67.18...7.6..1...8..25....52.68..716...7...8........  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56....1.2.43...4.3...26..4....5..5..63...7.81.....  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....56....1.2.43...4.31..2...4......25..63...7.81.5...  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....56....1.2.43...4.3...2...4......25..63...7.81.5...  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....56....1.2.43...4.31..26..4....5..5..63...7.81.....  ED=11.6/1.2/1.2
........1.....2.34235...6......78.6..8.23....7..5.6....26..78..3.8...7..57......2  ED=11.6/1.2/1.2
........1....23.45...6.738....3.6.....7.812...8.27.1...637.....17...8...2.8......  ED=11.6/1.2/1.2
........1....23.45...6.738....3.6.....7.812...8..7.1...637.2...17...8...2.8......  ED=11.6/1.2/1.2
........1.....2.34235...6......78.6..8.23....7..5.6.....6..78..3.8.2.7..57......2  ED=11.6/1.2/1.2
........1.....123.....245.6....654....32..1....41.3..2.16.52...3........78...6...  ED=11.6/1.2/1.2
........1....23.....4..5.....67...8..9......481.9..7.6.48.7.16.1.......876....4.9  ED=11.6/1.2/1.2
........1.......23...2456.....7.4..5..5.827...7..6.8...87....6.46...7...5.2..8...  ED=11.6/1.2/1.2
........1....23.....4..5.....67...8..97.....481.9....6.48.7.16..6....4.91......78  ED=11.6/1.2/1.2
........1.......2......3..4..526.7...27..8...36..75..8.835.7...27.63..8.5.6.8....  ED=11.6/1.2/1.2
........1.......2......3..4..5..6.....728.5..38..572.6.637.5...25.83..6.7.8.6....  ED=11.6/1.2/1.2
........1.......2......3..4..526.7...273.8...36..75..8.835.7...27.6...8.5.6.8....  ED=11.6/1.2/1.2
........1.......2......3..4..5.36.....782.5..38.5.72.6.63.75...25..8..6.7.86.....  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....98.6....6.25.9.7.7...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....98.6....6.25...7.7...8..69  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....98..7...6.25.9.7.7...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....98..7...6.25...7.7...8..69  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98.6....6.25.9.7.7..28..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98.6....6.25...7.7..28..69  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6.25.9.7.7..28..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6.25...7.7..28..69  ED=11.6/1.2/1.2
........1......234....25.....5.6..7..68..9...72.5.8.9..597.68..6.29.....87...2...  ED=11.6/1.2/1.2
........1......234....25.....5.6..78.6...9...72.5.8.9..597.68..6.29.....87...2...  ED=11.6/1.2/1.2
........1......234....25.....5.6..7..68..9...72.5.8.9..597.68...7...2...6.298....  ED=11.6/1.2/1.2
........1......234....25.....5.6..78.68..9...72.5...9..597.68...7...2...6.298....  ED=11.6/1.2/1.2
........1......234....25.....526..7..68..9...72.5.8.9..597.68..6.29.....87.......  ED=11.6/1.2/1.2
........1......234....25.....526..78.6...9...72.5.8.9..597.68..6.29.....87.......  ED=11.6/1.2/1.2
........1......234....25.....526..7..68..9...72.5.8.9..597.68...7.......6.298....  ED=11.6/1.2/1.2
........1......234....25.....526..78.68..9...72.5...9..597.68...7.......6.298....  ED=11.6/1.2/1.2
........1..2..3.....1245.....6...78..9......271.8..9.6..7.9.26..29.7.1..86......7  ED=11.6/1.2/1.2
........1..2..3.....1245.....6...78..9......271.8..9.6..7.9.26..29.7.1..86.....9.  ED=11.6/1.2/1.2
........1....23....45..6.....78...1..98....454..9..8.7.54.89.7.1.......478....5.9  ED=11.6/1.2/1.2
........1....23....45..6......7...89.78...4.55.98..1...54.879..1.......498.....57  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8..9.6.29.7.1..1.7.9.26.86......7  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8..9.6.29.7.1..1.7.9.26.86.....9.  ED=11.6/1.2/1.2
........1....23....45..6.....78...1..98....454..9..8.7.54.8..7.1.9.....478....5.9  ED=11.6/1.2/1.2
........1....23....45..6......7...89.78...4.55.98..1...54.8.9..1.7.....498.....57  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6.25...7.75.28..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98.6....6.25...7.75.28..6.  ED=11.6/1.2/1.2
........1.....234...2.3.5.6..4...6...6..53...7.8..6....1..652...2.1.4..3.4.3...5.  ED=11.6/1.2/1.2
........1.......23...2456.....7.4..5..5.827.6.7..6.8...87......46...7...5.26.8...  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6.25.9..87..2...6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....9...7...6.25....87..28..69  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....9...7...6.25.9..87..28..6.  ED=11.6/1.2/1.2
........1......234....25.....2..6....6.27..89.875.9....98......27..6....6.58.79..  ED=11.6/1.2/1.2
........1......234....25.....2..6....6..7..89.875.9....98..2...27..6....6.58.79..  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.97.....92..7...6.85.9...7..28..6.  ED=11.6/1.2/1.2
........1......234....25.....627..8..785.9...92...6....89......2.7.6....65.8.79..  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.97.....92..7...6.85.9...7...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6.7..8..785.9...92...6....89..2...2.7.6....65.8.79..  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....9...7...6.25....87...8..69  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....9...7...6.25.9..87...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6.25....87..2...69  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62.37..8..8572.6..2.6......73.6.5..8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62.37..8...6..8....8572.6..73.6.52..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62.37..8...6.......8572.6..73.6.52.8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62..7..8..8572.6..2.6.3....73.6.5..8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62..7..8...6.38....8572.6..73.6.52..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56....578.....62..7..8...6.3.....8572.6..73.6.52.8  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..453.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1.....2.34.25..........6....67.82.9..8.95.7....8.97....2...56.8.5.7..8.6.  ED=11.6/1.2/1.2
........1.....2.34.25..........6....67.82.9..8.95.7....8.97....2...56.8.5.7....69  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..453.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.3...61..21..453.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1.....2.34.25..........6....67.82.9..8.95.7....8.97....29..56.8.5.7....6.  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.1..453...3.2.61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.3...61..21..453.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1..453...3.2.61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1..1.23....45..6..........74.5..7819.9.....5.8..97......87....4541.8....9  ED=11.6/1.2/1.2
........1..1.23....45..6.....7.....4.5..8.19.98....5.7..98......7.....4541.7..8.9  ED=11.6/1.2/1.2
........1..1.23....45..6.....7....84.5..8.19.9.....5.7..98......78....4541.7....9  ED=11.6/1.2/1.2
........1....23.4...45.126......26.....3.415.45.61..3.5....6...7......2389.......  ED=11.6/1.2/1.2
........1....23.4...45.126......2......3.415.45.61..3.5....6...7......2389......6  ED=11.6/1.2/1.2
........1..2..3.....1245.......6..7..26.8.1.997......8..7...89..6......281.9..6.7  ED=11.6/1.2/1.2
........1..2..3.....1245.......67.8..26.9.1..78......9..8...97..6......291.7..6.8  ED=11.6/1.2/1.2
........1....23.45..4..126.....526.....3.41..45.61..3.5....6...7......2389.......  ED=11.6/1.2/1.2
........1....23.45..4..126.....52......3.41..45.61..3.5....6...7......2389......6  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1..45....3.2.61.....6.....7.....5..895...6..  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..45......6.....7.....5..895...6..  ED=11.6/1.2/1.2
........1....23....45..6.....4.7819.1.......59.7...4.8..8....54.9.7.....5.18..7.9  ED=11.6/1.2/1.2
........1....23.45.25.4.36.........6..741.....896.........5.1.42..3.....5...61.23  ED=11.6/1.2/1.2
........1....23....45..6.....4.78.9.1.......59.7...4.8..8....54.9.7...1.5.18..7.9  ED=11.6/1.2/1.2
........1..1.23....45..6.....78...1..9.....454..9..8.7.5..89.7.1.......478....5.9  ED=11.6/1.2/1.2
........1....23....45..6.....4.7819.1......759.....4.8.78....54.9.7.....5.18....9  ED=11.6/1.2/1.2
........1....23....45..6.....4.78.9.1......759.....4.8.78....54.9.7...1.5.18....9  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..45......65....7.....5..89....6..  ED=11.6/1.2/1.2
........1....23.4...45.126......26.4...3.415..5.61..3.5....6...7......2389.......  ED=11.6/1.2/1.2
........1....23.4...45.126......2..4...3.415..5.61..3.5....6...7......2389......6  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8..9.6.29.7.1.81...9..6.86......7  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8..9.6.29.7.1..1...98.6.86......7  ED=11.6/1.2/1.2
........1....23.45..4..126.....526.4...3.41...5.61..3.5....6...7......2389.......  ED=11.6/1.2/1.2
........1....23.45..4..126.....52..4...3.41...5.61..3.5....6...7......2389......6  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1..45.6..3.2.61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..45.6....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....23....45..6.....4.7.18.19......58.7...4.9..9....54.8.7.....5.19..7.8  ED=11.6/1.2/1.2
........1....23....45..6.....4.7..8.19......58.7...4.9..9....54.8.7...1.5.19..7.8  ED=11.6/1.2/1.2
........1..1.23....45..6.....78...1..9.....454..9..8.7.5..8..7.1.9.....478....5.9  ED=11.6/1.2/1.2
........1....23....45..6.....4.7.18.19.....758.....4.9.79....54.8.7.....5.19....8  ED=11.6/1.2/1.2
........1....23....45..6.....4.7..8.19.....758.....4.9.79....54.8.7...1.5.19....8  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.3...61..21..45.6....65....7.....5..89.......  ED=11.6/1.2/1.2
........1.....2.34.25........6....7..8.69....29.5.7.8..5.7.9...76.28.9..8...56...  ED=11.6/1.2/1.2
........1.....2.34.25........6....78.9..6....28..57.9..5..78...76.92.8..9..5.6...  ED=11.6/1.2/1.2
........1.....2.34.25........6....7..8.69....29.5.7.8..5.7.....76.28.9..8.9.56...  ED=11.6/1.2/1.2
........1.....2.34.25........6....78.9.68....2..5.7.9..5.7.....76.29.8..9.8.56...  ED=11.6/1.2/1.2
........1.....2.34.25..........67...68.92.7..9..5.8....9.78....27..56.9.5.8....6.  ED=11.6/1.2/1.2
........1.....2.34.25..........67...68.92.7..9..5.8....9..8....27..56.9.5.8....67  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1..453...3...61.....6.....7.....5..895...6..  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.1..453...3...61.....6.....7.....5..895...6..  ED=11.6/1.2/1.2
........1....23....45..6.....78...1..98....454..9....7.54.89.7.1......847.....5.9  ED=11.6/1.2/1.2
........1....23....45..6......7....8.79....455.89...1..54.97.8.1......948.....5.7  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1..4536..3...61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.1..4536..3...61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....23....45..6.....78...1..98....454..9....7.54.8..7.1.9....847.....5.9  ED=11.6/1.2/1.2
........1....23....45..6......7....8.79....455.89...1..54.9..8.1.7....948.....5.7  ED=11.6/1.2/1.2
........1.....2.34.25..........6....67.82.9..8.95.7.....697....2...56.8.5.7..8.6.  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...2..1..453..4..2.61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1...234.....2..5.....6....7..89.....271.9..8.6..7.8..6..68...1.992......7  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7.28..87...1.99.......6.79......2.8....6.61.9..7.8  ED=11.6/1.2/1.2

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........1....2345...24.1.36...3...2..1..453..4..2.61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....23.45..21.436......5..4...3..1...5..16.232.......67..4.....8.96.....  ED=11.6/1.2/1.2
........1....23.45..21.436.........6.7.4......896..........5..42..3..1..5...16.23  ED=11.6/1.2/1.2
........1....23.....4..5.....67...8..97....1481.9....6.48.7..6..6....4.91......78  ED=11.6/1.2/1.2
........1....23.....4..5.....67...8..9.....1481.9..7.6.48.7..6.1.......876....4.9  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.4...61..12...53.....65.....7....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1...53..4..2.61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...2..4...61..12..453.....65.....7....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...2..4...61..12..453.....6......7....5..895......  ED=11.6/1.2/1.2
........1....23.45.25.1.36.........4..7.6....689..........52......63.1..5..1.4.23  ED=11.6/1.2/1.2
........1....2345...241..36...26.1.4...3...2..1..543.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8...96..7.9.6...69....1882......7  ED=11.6/1.2/1.2
........1....23.45.25.1.36.......6.4..7.6.....89..........52......63.1..5..1.4.23  ED=11.6/1.2/1.2
..............1..2....34.56..47.3....17.89...93..4.8...79......18.......4.3.17.9.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....9...7...6..5...787..28..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98..7...6..5...787..2...6.  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....9...7...6..5...787...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6..2....756.89..82.79.....9..6....6..5...787...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....98.6....6..5...787..2...6.  ED=11.6/1.2/1.2
........1......234....25.....6.......756.89..82.79.....9..6....6..5...787..28..6.  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...2..1..453..43...61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.1...53..43...61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...24.1...53..43...61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..2..1..453..43...61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36...3...2..1..453..43...61.....65....7.....5..89.......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..24.1...53..43...61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....2345...24.1.36....1..2..1..453..43...61.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1.....2345.23....6...2.67.....893....97...86...697.....28...9...3.7.86..2  ED=11.6/1.2/1.2
........1......234....25.6...75.8....8629...595..76....69......5.87.96..72..8....  ED=11.6/1.2/1.2
........1.....2345.23....6.....67.....893....97.2.86...697.....28...9...3.7.86..2  ED=11.6/1.2/1.2
........1......234....25.6...7..8....8629...595..76....69.5....5.87.96..72..8....  ED=11.6/1.2/1.2
........1.....2345.23....6...2.67.....893....97...86...6972.....8...9...3.7.86..2  ED=11.6/1.2/1.2
........1.......23....245.6..7.8..4..29.41...48.9.7.1..9.7.....21...8...7.8.92..4  ED=11.6/1.2/1.2
........1.......23....245.6..7.8..4..29.41....8.9.7.1..947.....21...8...7.8.92..4  ED=11.6/1.2/1.2
........1.......23....245.6..7.8..4..29..1...48.9.7.1..947.....21.4.8...7.8.92...  ED=11.6/1.2/1.2
........1.......23....245.6..7.8..4..29..1...48.9.7.1..9.7.....21.4.8...7.8.92..4  ED=11.6/1.2/1.2
........1.......23....245.6..7.8..4..29.41....8.9.7.1..947.....21.4.8...7.8.92...  ED=11.6/1.2/1.2
........1......234.....5.....6.27.8..7895....92.6.8....8.5.2...2.7.96...65.87.9..  ED=11.6/1.2/1.2
........1......234.....5.....6.27.8..7895....92.6.8....895.2...2.7..6...65.87.9..  ED=11.6/1.2/1.2
........1....23.45..21.436.....16.54...2.5..3.5.34.12.2.......67..4.....8.96.....  ED=11.6/1.2/1.2
........1...234.....2..5..........67..6.782.9.97...18..78....122.9.....661.8..97.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7..28.87...91.9.....6.7.79...1.22.8.....661.9..78.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7..28.87...91.9.....6.7.7....1.22.8....9661.9..78.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.....7.89....1271.9..68...7.8.2.6.68...19.92.....78  ED=11.6/1.2/1.2
........1...234.....2..5.....6....78.9....1.281.7..96...8.9..26.69...71.72....8.9  ED=11.6/1.2/1.2
........1..2..3.....1.45..........67.27.6.18..8....2.9.96.....82.89..67.71.6..9.2  ED=11.6/1.2/1.2
........1....23.....4..5....1.....674.7.6.18.8.....4.9.489..67.17.6..9.49.6.....8  ED=11.6/1.2/1.2
........1....23.....4..5....1.....674.7.6..8.8.....4.9.489..67.17.6..9.49.6....18  ED=11.6/1.2/1.2
........1......234....25.....2.67....6...8.79.7859.....97.52...28...6...6.587.9..  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7859....92..68....8..52...2.79.6...65.78.9..  ED=11.6/1.2/1.2
........1......234.....5.....2.67....6.2.8.79.7859.....97.52...28...6...6.587.9..  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7859....92..68....89.52...2.7..6...65.78.9..  ED=11.6/1.2/1.2
........1.....2.34..2.1356......6.43....241.5.4.35..2.2.......67...31...8.9.65...  ED=11.6/1.2/1.2
........1.....2.34..2.1356.....241.5...1.6.43.4.35..2.2.......67...3....8.9.65...  ED=11.6/1.2/1.2
........1.....2.34..2.1356......6.43....241.5.4.35.62.2........7...31...8.9.65...  ED=11.6/1.2/1.2
..............1.23....45..6.14.578..5.819....79.8.4....715.9.4.8.5......94..7....  ED=11.6/1.2/1.2
..............1.23....45..6..7....8..39...2..86..2.3.7.93...67.62.9...387.8...9.2  ED=11.6/1.2/1.2
..............1.23....45..6..7....8..39...26.86..2.3.7.93....7.62.9...387.8...9.2  ED=11.6/1.2/1.2
..............1.23....45..6.14.578..5.8.9....79.8.4....715.9.4.8.5.1....94..7....  ED=11.6/1.2/1.2
........1.....2.34....56.....16......56.781..72...18...872.....5.2.67..861.8.5...  ED=11.6/1.2/1.2
........1.....2.34....56.....162.....56.781..72...18...87......5.2.67..861.8.5...  ED=11.6/1.2/1.2
........1.....2.34....56.....1.......56.781..72.5.18...872.....5.2.67..861.8.5...  ED=11.6/1.2/1.2
........1.....2.34....56.....1.2.....56.781..72.5.18...87......5.2.67..861.8.5...  ED=11.6/1.2/1.2
........1.....2.34.23........523.....6..75.8.3.76.8....32.567.87...2....8.6..75..  ED=11.6/1.2/1.2
........1.....2.34.23........523.....6..75.8.3.76.8....32.567.8.5..2....8.6..75..  ED=11.6/1.2/1.2
........1.....2.34.23........523.....6..75.8.3.76.8....32.567..7..82....8.6..75..  ED=11.6/1.2/1.2
........1.....2.34.23........523.....6..75.8.3.76.8....32.567...5.82....8.6..75..  ED=11.6/1.2/1.2
........1.......23.....45....567.8...864.2...74..85....58..6.7.42...8...6.752....  ED=11.6/1.2/1.2
........1.......23.....45....567.8...86..2...74..85....58.46.7.42...8...6.752....  ED=11.6/1.2/1.2
........1.....2.34235........2.67.8.6..5.8...7..23.....28..67..3.7..56.856.......  ED=11.6/1.2/1.2
........1.....2.34....56.....267.1...658.17..7...258...87......52..68..76.1......  ED=11.6/1.2/1.2
........1.....2.34....56.....1.257...2.68.1...567.18...87......5.2.67..861.......  ED=11.6/1.2/1.2
........1.....2.34235..........67.8.6.35.8...7..23.....28..67..3.7..56.856.......  ED=11.6/1.2/1.2
........1.......23...2456.....7.4..5..4.827.6..756.8...46..7...25.6.8...7.8......  ED=11.6/1.2/1.2
........1.....2.34....562....267.1...658.1...7...258...87......52..68..76.1......  ED=11.6/1.2/1.2
........1.....2.34.35...6....2.78.6.7..5.6...8..23.....26..78..3.8..57.657.......  ED=11.6/1.2/1.2
........1......234....25.....65.7.8..7829....95..6.....89......5.79.68..62.87....  ED=11.6/1.2/1.2
........1......234....25.....65.7.8..7829....95..68....89......5.79.68..62..7....  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7829....95..68....89.5....5.79.68..62..7....  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7829....95..6.....89.5....5.79.68..62.87....  ED=11.6/1.2/1.2
........1......234.....2..5..6.78....9.25....72.6.9..8.67.9.5..85...6...9.2..78..  ED=11.6/1.2/1.2
........1......234.....2..5..5..6....7689.5..82...79...6.7......9852....7.2.68..9  ED=11.6/1.2/1.2
........1......234.....2..5..6.78....9825....72.6.9....67.9.5..85...6...9.2..78..  ED=11.6/1.2/1.2
........1......234.....2..5..5..6....7689.5..82...79...6.7.9....9852....7.2.68...  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.18....7.69.1...689.....21..7....9.7.26..8  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.1....87.69.1...6.9.....21.87....9.7.26..8  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.18....7.69.1...689.....21.87....9.7.26...  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.1....87.69.1...689.....21.87....9.7.26...  ED=11.6/1.2/1.2
........1......234.....2..5..6.78....8925....72.6.9....679..5..85...7...9.2..68..  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.18...7..96.1...986.....21.7.....6.7.29..8  ED=11.6/1.2/1.2
........1......234.....2..5..6.78.....925....27.6.9..8.92..68..58...7...6.79..5..  ED=11.6/1.2/1.2
........1......234.....2..5..6..78...29.18...7..96.1...986.....21.78....6.7.29...  ED=11.6/1.2/1.2
........1......234....25.....65.7.8..5829....97..6.....89.7....5.76.98..62.8.....  ED=11.6/1.2/1.2
........1......234....25.....65.7.8..5829....97..68....89.7....5.76.98..62.......  ED=11.6/1.2/1.2
........1....23.45..21.436.........6.7.4......896..........5..32...16.545..34.12.  ED=11.6/1.2/1.2
........1....23.....4..5....1......64.6.7.18.87....4.9.489..76.16.7..9.49.......8  ED=11.6/1.2/1.2
........1....23.....4..5....1......64.6.7..8.87....4.9.489..76.16.7..9.49......18  ED=11.6/1.2/1.2
........1.....2.34..2.1356.........6.7..3.....89.65........41.52..1.6.434..35..2.  ED=11.6/1.2/1.2
........1.....2.34..2.1356.........6.7..31....89.65........41.52....6.434..35..2.  ED=11.6/1.2/1.2
........1......234....25.....6..2....758.69..82.97.....92.67...6.85.9...7...8..6.  ED=11.6/1.2/1.2
........1......234....25.....6.......758.69..82.97.....92.67...6.85.9...7..28..6.  ED=11.6/1.2/1.2
........1......234....25.....2.67....685.9....7..8..69.96..2...28..7....7.58.69..  ED=11.6/1.2/1.2
........1......234....25.....6.7..8..785.9...92..86....89..2...2.7.6....65.7.89..  ED=11.6/1.2/1.2
........1......234....25.....2.67....685.9....7.28..69.96......28..7....7.58.69..  ED=11.6/1.2/1.2
........1......234....25.....627..8..785.9...92..86....89......2.7.6....65.7.89..  ED=11.6/1.2/1.2
........1.....2.34..2.1356.....241.5...1.6.43.4.35..2.2.......67....5...8.9.6....  ED=11.6/1.2/1.2
........1.....2.34..2.1356.........6.7...5....89.6........241.52..1.6.434..35..2.  ED=11.6/1.2/1.2
........1.......2......3..4..3.56..7.6.28.5..25...7....86.7....5.283..7.73.6.5.8.  ED=11.6/1.2/1.2
........1.......2......3..4..3.562.7.5...7....6.28.5...86.7....5.283..7.73.6.5.8.  ED=11.6/1.2/1.2
........1.......2......3..4..5.6.....7283..6.36.5.7.8..83.75..65..28.7..72...6...  ED=11.6/1.2/1.2
........1.......2......3..4..3.56..7.6.28.5..25.3.7....86.7....5.28...7.73.6.5.8.  ED=11.6/1.2/1.2
........1.......2......3..4..3.562.7.5.3.7....6.28.5...86.7....5.28...7.73.6.5.8.  ED=11.6/1.2/1.2
........1.......2......3..4..5.6.....728...6.36.5.7.8..83.75..65..28.7..72.3.6...  ED=11.6/1.2/1.2
........1.......2......3..4..5..6.....728.5..38..572.6.637.5.8.25.83..6.7...6....  ED=11.6/1.2/1.2
........1.......2......3..4..5.36.....782.5..38.5.72.6.63.75.8.25..8..6.7..6.....  ED=11.6/1.2/1.2
........1.......23...2456.....7.4..5..4.827....756.8...46..7...25...8...7.8....6.  ED=11.6/1.2/1.2
........1.....234...2.315.6....53.....4...6...78..6...1...652..2..1.4.534..3.....  ED=11.6/1.2/1.2
........1.....2.34....56.....26..1...657.18..8...257...7.......52..67..86.1..8...  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7.29....95..68....8..5....5.76.9...62.87.9..  ED=11.6/1.2/1.2
........1......234....25.....6..7.8..7.29....95..68....89.5....5.76.....62.87.9..  ED=11.6/1.2/1.2
........1..2..3.....1245..........67..6.781.9.9....28..78......1.9...6..62.8..79.  ED=11.6/1.2/1.2
........1....23.45.251..36......51.4....16.232..34.....5......6.7.4......896.....  ED=11.6/1.2/1.2
........1..2..3.....1245.....6....78.9....1..72.8..69...7.98..6.6.....2.81....7.9  ED=11.6/1.2/1.2
........1...234.....2..5.....6.78..9.1.....67.9....28..78....1.1.9...6..62.8..79.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.78.19.1....6.7.9....82..78......1.9....6.62.8..97.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.78..9.9.....2.81....6.7.7....1..1.9....6862.8..97.  ED=11.6/1.2/1.2
........1......234....25.....6..7.89.7.2.....95..68....8..5....5.76.9...62.87.9..  ED=11.6/1.2/1.2
........1..2..3.....1245.....6.7..18.8....92.9.....6.7.79......1.8....6.62.9..87.  ED=11.6/1.2/1.2
........1..2..3.....1245.....6....7..89...1..72.9..68...7.8...6.6....92.91....7.8  ED=11.6/1.2/1.2
........1..2..3.....1245.....6....78.9....1..72.8..69...7.9...6.6....82.81....7.9  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7...8.8....29.91.....67.79....1.1.8...6..62.9..78.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7..18.8....92.91....6.7.79......1.8....6.62.9..87.  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7...8.8....29.91.....67.7.....1.1.8...6.962.9..78.  ED=11.6/1.2/1.2
........1......234....25.....5.67.....829.....6...8.79.97.5....58.6.....6.278.9..  ED=11.6/1.2/1.2
........1......234....25.....5.67.....829.....6.5.8.79.97......58.6.....6.278.9..  ED=11.6/1.2/1.2
........1...234.....2..5.....6...78..9......271.8...69..7.9.6...69....1882....9.7  ED=11.6/1.2/1.2
........1...234.....2..5..........67..7.6829..96...1.8.68......2.9....7.71.8..9.6  ED=11.6/1.2/1.2
........1...234.....2..5.....6.7.28..87...1.99......76.79......2.8....6.61.9..8.7  ED=11.6/1.2/1.2
........1....23.....4..5....1.....674.7.6..8.8.....4.9.486...7.17.9....49.6....18  ED=11.6/1.2/1.2
........1..2..3.....1.45..........67.27.6.18..8....2.9.96.....82.86...7.71.9....2  ED=11.6/1.2/1.2
........1....23.....4..5....1.....674.7.6.18.8.....4.9.486...7.17.9....49.6.....8  ED=11.6/1.2/1.2
........1....23.....4..5....1......64.6.7..8.87....4.9.487...6.16.9..7.49......18  ED=11.6/1.2/1.2
........1....23.45..21.436.........6.7.4......896..........5..32..34.1..5...16.24  ED=11.6/1.2/1.2
........1....23.....4..5....1......64.6.7.18.87....4.9.487...6.16.9..7.49.......8  ED=11.6/1.2/1.2
........1....2345...214..36...26.1.4...3.1.2..1..543.....6.....7.....5..895......  ED=11.6/1.2/1.2
........1....23.45..21.436......5..3...34.1...5..16.242.......67..4.....8.96.....  ED=11.6/1.2/1.2
........1...234.....2..5.....6....7..89.....271.9..6.8..7.8..6..68...1.992.....87  ED=11.6/1.2/1.2
........1.......2......3..4..3.56..7.6728.5..25........3.6.5.8..86.7....5.283..7.  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..578.....62.37..8...6..8....3.6.52...8572.6..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..578.....62.37..8...6.......3.6.52.8.8572.6..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62.37..8..8572.6..2.6......73.6.5..8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62.37..8...6..8....8572.6..73.6.52..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62.37..8...6.......8572.6..73.6.52.8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56..7.6728.5..25.3......3.6.5.8..86.7....5.28...7.  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..578.....62..7..8...6.38....3.6.52...8572.6..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..578.....62..7..8...6.3.....3.6.52.8.8572.6..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62..7..8..8572.6..2.6.3....73.6.5..8  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62..7..8...6.38....8572.6..73.6.52..  ED=11.6/1.2/1.2
........1.......2......3..4..3.56.7..5.8.....62..7..8...6.3.....8572.6..73.6.52.8  ED=11.6/1.2/1.2
........1.....2.34.23........5.3......67.8...27..65.8..3..576...5.82....8.7..65..  ED=11.6/1.2/1.2
........1.....2.34.23........5.3......67.8...27..65.8..3..576..6..82....8.7..65..  ED=11.6/1.2/1.2
........1.....2.34....56.....72......52.67..816.8.5....8.6.....27...18..5.6.7.1..  ED=11.6/1.2/1.2
........1.....2.34....56.....7.......52.67..816.8.5....8.62....27...18..5.6.7.1..  ED=11.6/1.2/1.2
........1.....2.34....56.....7.......52.67..816.8.5....8..2....27.5.18..5.6.7.1..  ED=11.6/1.2/1.2
........1.....2.34.23........5.3......67.8...27..65.8..3..576.86...2....8.7..65..  ED=11.6/1.2/1.2
........1.....2.34.23........5.3......67.8...27..65.8..3..576.8.5..2....8.7..65..  ED=11.6/1.2/1.2
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Re: The hardest sudokus (new thread)

Postby eleven » Tue Mar 15, 2022 12:47 am

The first two 11.8's are nice samples for solving without pencilmarks.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 15, 2022 7:40 am

coloin wrote:On page 55 of this thread
There are 6 ways to fill in the 4th box (B5)
3 ways are possible to use the 3 clues
3 ways it is not possible to use all 3 clues the diagonal pattern is equivalent … but not in the context of the other 3 boxes ( B1B2B4)
The 3 ways that are impossible would have the hamner pattern with the handle ( albeit offset in 2 of the 3 cases)


OK. I added the reference to the list in the "tridagon" thread.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 15, 2022 8:16 am

mith wrote:
Code: Select all
........1.....2.......3..45..1.23....2671.8..73.6.81...8.......2.3.86..761..7....  ED=11.9/1.2/1.2
........1.....2.......3..45..6.......71.8....32..67..8.6..23....837..1..7.281.6..  ED=11.9/1.2/1.2
........1.....2.34....562....1.257...267.18...5.68.1...87......5.2.68..761...7...  ED=11.8/1.2/1.2
........1.....2.34235...6......78.6..8.53....3.72.6....72......65...78..8.3.257.6  ED=11.8/1.2/1.2

....


Wow, 2 new 11.9s and a whole lot (38) of new 11.8s, many of which are not in T&E(2).

Are they all independent, i.e. did you stick to your decision to publish here only the minlex form of expanded puzzles?

Here the list of those (24) not in T&E(2):
Code: Select all
........1.....2.......3..45..1.23....2671.8..73.6.81...8.......2.3.86..761..7....  ED=11.9/1.2/1.2 not in T&E(2)
........1.....2.......3..45..6.......71.8....32..67..8.6..23....837..1..7.281.6..  ED=11.9/1.2/1.2 not in T&E(2)
........1.....2.34....562....1.257...267.18...5.68.1...87......5.2.68..761...7...  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34235...6......78.6..8.53....3.72.6....72......65...78..8.3.257.6  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....1.25....267.18..75.68.1...8.......5.2.68..761...7...  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....7.......61..8...25..67..8.7..25....856..1..6.28.17..  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....56..1...627.18..8...257...7.......52..68..76.1..7...  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34..2.3156.....564...1.2.43.6.4.31..2.....6......4....5.7.8..5...  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....56..1...627.18..8...257...7.......52..6...86.1..8...  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34..2.3156.....56.1..1.2.43.6.4.3...2.....6......4....5.7.8..5...  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34.23...5....623.....7.8.5...2.8.76.5..87......5.2..76..63...87.5  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34.23...5....6.78.5...823....37.6.5....67......5.2..78..83...67.5  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....7.25....5867.1..62.8.17...16......2.5.68..787.......  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....1.25....267.18..75.68.1...87......5.2.67..861.......  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34.23...5....6.78....5823.....7.6.5....67.....25.2..78..83...67.5  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34.23...5....6.78....5823.....7.6.5....67.....25....78..83..267.5  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....7.......52.67..816...8....8..25...2.67.18..57.6..1..  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34....562....567.1...628.17..7...258...87......52..6...76.1......  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34235...6....2.78.6..8.23....7..5.6....26..78..3.8...7.657.......  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34235...6......78.6..8.23....7.35.6....26..78..3.8...7.657.......  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34....562....1.257...267.18...5.68.1...87......5.2.6...861.......  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon
........1.....2.34.23...5....6.78.5...823.....7.6.5....67.....25....78..83..267..  ED=11.8/1.2/1.2 not in T&E(2)
........1.....2.34.23...5....6.78.5...823.....7.6.5....67.....25.2..78..83...67..  ED=11.8/1.2/1.2 not in T&E(2)
........1.....234...2.315.6....652...2.1.4..3.4.3..15...4...6...6..53...7.8..6...  ED=11.8/1.2/1.2 not in T&E(2)

[Edit 1]: I added the information about those that don't have a tridagon (all those in T&E(2) have one).
[Edit 2]: All the puzzles that have a tridagon, including all those in T&E(2), can be solved with it + whips.
[Edit 3]: As with mith's previous series, all the puzzles can be solved in T&E(W2, 2)
Last edited by denis_berthier on Tue Mar 15, 2022 11:31 am, edited 3 times in total.
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Re: The hardest sudokus (new thread)

Postby hendrik_monard » Tue Mar 15, 2022 9:44 am

Congratulations to mith for this long list of puzzles of which many are apparently not in T&E(2).
All these 618 puzzles are minimal. I didn't check the SER however.
May I also remark that the very first puzzle in the list is a morph of the one I posted last Saturday. I have to admit however that the one I posted is a spin off from one of the two puzzles not in T&E(2) posted by mith on February 28th.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 15, 2022 9:52 am

hendrik_monard wrote:Congratulations to mith for this long list of puzzles of which many are apparently not in T&E(2).
All these 618 puzzles are minimal. I didn't check the SER however.
May I also remark that the very first puzzle in the list is a morph of the one I posted last Saturday. I have to admit however that the one I posted is a spin off from one of the two puzzles not in T&E(2) posted by mith on February 28th.

Hi Hendrik,
did you check if some have the same minlex expanded version?
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Re: The hardest sudokus (new thread)

Postby eleven » Tue Mar 15, 2022 11:08 am

denis_berthier wrote:
Code: Select all
........1.....2.34....562....56..1...627.18..8...257...7.......52..68..76.1..7...  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon

Here the extra candidate 8 can be eliminated.
Hidden Text: Show
Code: Select all
+-------------------------+-------------------------+--------------------------+
| 2      h34589   346789  | 3489    3479    349     | e569     56789   1       |
|g19     h589     6789    | 189     179     2       | e569     3       4       |
|g1349   g3489   g34789   | 13489   5       6       |  2      f789    f89      |
+-------------------------+-------------------------+--------------------------+
| 7       349     5       | 6       8       349     |  1       249     239     |
| 349     6       2       | 7       349     1       |  8       459     359     |
| 8       1       349     | 349     2       5       |  7       469     369     |
+-------------------------+-------------------------+--------------------------+
| 349     7      a3489    | 25      1349    349     | d34569   125689  25689   |
| 5       2       349     | 349+1   6       8       | d349     19      7       |
| 6      b349+8   1       |c25      349     7       | d3459   c2589   c2589    |
+-------------------------+-------------------------+--------------------------+

8r7c3 = r9c2 - (8=259)r9c489 - r789c7 = 9r12c7 - (9=87)r3c89 - (7|8 = 1349)b1p4789 - (3|4|9 = 58)r12c2 => -8r9c2
Then trivalue oddagon 349 => 1r8c4, stte
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 15, 2022 11:51 am

eleven wrote:
denis_berthier wrote:
Code: Select all
........1.....2.34....562....56..1...627.18..8...257...7.......52..68..76.1..7...  ED=11.8/1.2/1.2 not in T&E(2) No Tridagon

Here the extra candidate 8 can be eliminated.
Hidden Text: Show
Code: Select all
+-------------------------+-------------------------+--------------------------+
| 2      h34589   346789  | 3489    3479    349     | e569     56789   1       |
|g19     h589     6789    | 189     179     2       | e569     3       4       |
|g1349   g3489   g34789   | 13489   5       6       |  2      f789    f89      |
+-------------------------+-------------------------+--------------------------+
| 7       349     5       | 6       8       349     |  1       249     239     |
| 349     6       2       | 7       349     1       |  8       459     359     |
| 8       1       349     | 349     2       5       |  7       469     369     |
+-------------------------+-------------------------+--------------------------+
| 349     7      a3489    | 25      1349    349     | d34569   125689  25689   |
| 5       2       349     | 349+1   6       8       | d349     19      7       |
| 6      b349+8   1       |c25      349     7       | d3459   c2589   c2589    |
+-------------------------+-------------------------+--------------------------+

8r7c3 = r9c2 - (8=259)r9c489 - r789c7 = 9r12c7 - (9=87)r3c89 - (7|8 = 1349)b1p4789 - (3|4|9 = 58)r12c2 => -8r9c2
Then trivalue oddagon 349 => 1r8c4, stte

Are you sure it satisfies the parity conditions??
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