## A record named "maximum" of Sudoku list

Everything about Sudoku that doesn't fit in one of the other sections
Mike Barker, I am still interested in how your solver handle the puzzle. Let me rephrase my request: as you have stated that the puzzle have 9 Unique Rectangles, show me how your program use them to solve the puzzle.

Mike Barker wrote:It reports the first technique that is found which is why my solutions tend to be longer.(...) however, there is an elegance in short solutions.

A shorter solution isn't necessarily a more elegant solution.

Now, I am interested on how human solvers would tackle this puzzle.
Thanks, Carcul
Carcul

Posts: 724
Joined: 04 November 2005

### Re: re: "naked single" valid, "hidden single&

Pat wrote:
gsf wrote:I re-ran Gordon's 18-clue puzzles
with the invalid qualification:
Code: Select all
`-qF-G -Q!N -e V`

( "naked single" valid and "hidden single" invalid ): 66 puzzles
this is the rarest type - could we please have an example?

here are all 66
Code: Select all
`1...32.8.6.97..1...........3..9..6...2..4...3..........5.....2....6......7.......1...32.8.6.97..1...........3..9..6...2..4...5..........5.....2....6......7.......1...32.8.6.97..1...........3..9..6...2..4...8..........5.....2....6......7.......1...3..47.3..658...........9.72...........61....8.....4..7......6....5...........1..3..7...52.4.............3..7..6.........45......1...4..52.8.7.....3...........1...3..97.3..658...........9.72...........61....8.....4..7......6....5............1.4..3......2..8.....7....9.4....7....15.2.....3.....7...6..2....5..1...........1...5.3.7.5..28.............2...6.8.....7.9.....4.....9..6..4.........2....3.....1...5.3.9.5..27.............2...6.7.....1.8.....4.....8..6..4.........2....3......1..5..7....8....9.........2..6..8.....3......7.........6.71.4.8.5.4.2...........1....5.79.5..438...........7..9...6..3..1.4...........9..2...........3.....8......174...5..5..236...........23..8.......7...1.......2..4.....8.....1.....9........1...7.......8..4........9....2.6..1..8.3......4..5....6...1..5....4..8.....9.....1...7.......8..9........4....2.6..1..8.3......4..5....6...1..5....4..8.....9......184...5..5..726...........27..3.......8...1.......3..9.....2.....1.....4.........18.5.4...5.6...72...............81.2..3......7.......4..2....3......1..9.........185...6..6..237...........23..4.......8...1.......4..5.....2.....1.....9.........23.6.5...6.7...18.........18.....4......23.....4.....5..1...........2..9.........23.6.5...6.7...18.........81.....4......23.....4.....5..8...........2..9........2..4.1.......3.7...........4..2...6.......3..8.........37.5...2.5.6...41............2..4.51...........3......54.9.6...7..18.9..........8....2.1.6...........5........2..4.51...........3......54.9.6...7..18.9..........8....3.1.6...........5......246...7..7..35..8...........84...2.3...9.5...........1.....3.....2.....6........24.7........9...3..1......83.8.2..5.....146...........7..3...........1..5.........2..56..34..1..7............65.3....1..7...........4.......2.6.7..4.....8.........2..56..34..1..8............65.3....1..8...........4.......2.6.7..4.....8.........2...6.453..9..1...............4..2.9.....3..8.....9...45.....6...3.....1..........2.6..718..5...........4...1.....265..3..............3..4..5......21...4.........3.....1....2..4.............1.3..6.4..7..5........2...6..81.3.2.....7..5..........3.2..5....6..7..4.....8.....7..4...2.....3...........5..31.2.7.....6..8........3...4.8...9.7...2...........275...6..6..83..4.........1.....3.....2.....5........3...4.9...8.7...2...........275...6..6..83..4.........1.....3.....2.....5........3...4.9...8.7...2...........275...8..6..93..4.........1.....3.....2.....5...............35...1........8.....6..2..4..1.....8..2.........7..3...9.4..9..2..8....1..3..5..1.........42......8..5..1..3...4..62.............62.4..7....3..5...........3...5.7...8.2.................8...3.7.....9........4..1...37..6.6.4...28.........3...5.7...8.2.................8...3.7.....9........4..1...73..6.6.4...28.........3...8..4..7....6...1..........1..7...6....5..4......8.8.2.4...3...7..1............385...4...4.216...........7.....1..52..........8.....1...9...2...3...8..............41....2....9..63.......5......4.......2...6.......1.87...5....2..7..4...6....4.1.5..3.2......68...3.........4.1..36.............2...8.6......7.5...........4...41..7.......2.3..5.....8.....1...4.3.....2............7.6.4.1.2...3..........5...4.2....89.....1..............6..8.....5...2.1........6...197...82.7..3...........4.6..1..8...2...............2.7...3....9..........4...5.4.1.7.3..5...62.........4.....6.5...3.....9.........37.8..9.....562...1.........97...3....2.....5.........49.5..3..3.6.27...........5..8..2..1............4....2.....8.....49.....6.......5......1...63........4..7...2..18.....7...3.....6.....18..2...5...7..6............5.2...3.....6.4..1.........3.5.8..2......6..4........6...4.1.....3...5.......7..5..3..2.........1....9......1.....84...5.....3.........6..185..2...6.3.7..........5.3...8.1...7.4............832...5..6..417...........9.......1...8.....2.........5.3...9.1...7.4............932...5..6..817...........4.......1...9.....2...........57..2.84..1...........6....2...9.1...................7.3.1....26..5...3....8.........57...4........3.....3..2..4..1.....6..2.........8..5...9.6..9..2..4....3..6...2.....3....7.....8..4...1.3.7.6.5..1...29.........2...9..........3......4....6...3.1...8.7...2...........274...5..5..19..8.........1.....3.....2.....4........6...3.1...9.7...2...........274...5..5..81..9.........1.....3.....2.....4.........63..7.1.2..4..5...........4..5..2......1...78.........1.....73...2.....5.........6.3...8.1...7.4............832...5..5..417...........9.......1...8.....2.........6.3...8.1...7.4............832...5..5..617...........4.......1...8.....2.........6.3...8.1...7.4............832...5..5..617...........9.......1...8.....2.........6.3...8.1...9.4............832...5..5..617...........4.......1...8.....2.........6.3...9.1...7.4............932...5..5..817...........4.......1...9.....2........6....5.9..8....3...4.......1..8...5..7.4...........8.....62.4..51.......9........6...7..4..2.3..5............5.2..3..4.......7......8..7.1.4..6....5..2............7....2..4...8.......1.....5...6..8..1.3......2..........2..9.56...7....84........8..7..147...95.6..........2.....5.....6..3.....1......1.4...8.5.....9...........`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Mike Barker wrote:I think we'd all like to find an algorithm to find the backdoor. As far as I know this is an area which is wide open and ripe for focus of the BB's considerable talent.

right
and we have to be careful what we ask for
because all known 9x9 sudoku have at most a backdoor of size two (2 cells solved trivially solves the puzzle),
"optimal" non-trivial solutions (moves required beyond the agreed-upon basic techniques)
all have either 0, 1, or 2 moves

the current state of the art for determining the optimal moves straight away is indistinguishable from guessing
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Hi Eioru,

since the solution methods don't show up at all in your list until now, I'd like to add a puzzle with UR type 4 (ER9.2):
Code: Select all
`7..8......2..9.3.......4.1.3.....6...5..8..9...1..2..4.6.5.......9.1..2......3..7`

one with BUG type 1 (ER 9.0):
Code: Select all
`5..7..8...6..4..1...3..2..7..48..2...1..3.........9..4..86..3...3..2..5.9....5..6`

and one with BUG type 2 (ER 9.0):
Code: Select all
`..26..4...3..9..8.1....2..73.....5...4..7..2...1..5..46..5......9..2...3..7..3.9.`

I like the idea of your list. Oh, btw, could you edit your "contration" into "contradiction". Just a typo, but as you are editing your list anyway...

Kind regards, Maria
Last edited by maria45 on Mon Sep 25, 2006 5:21 pm, edited 1 time in total.
maria45

Posts: 54
Joined: 23 October 2005

Hi Carcul,

concerning your puzzle: I solved it with 2 forcing chains, 1 naked triple, 3 naked pairs, 2 pointing, 1 claiming and singles.

Kind regards, Maria
maria45

Posts: 54
Joined: 23 October 2005

Again, these UR's exist, they are not necessarily required. For a description of the UR types see here and here. Note also most ALS types appear latter in my solver. ALS xz-rule with a bivalue cell is intermediate with the idea that the bivalue can clue the search for the ALS. I have no data to back up this assertion.
Code: Select all
`Locked Row Line/Box Pair: r1c45 => r1c1<>26,r1c2<>6,r1c9<>2Locked Row Line/Box: r8c56 => r8c3<>8Locked Row Line/Box: r5c79 => r5c1<>3Locked Column Line/Box: r23c9 => r5c9<>2Locked Column Box/Box: r37c1|r3789c3 => r45c1<>6,r4c3<>6Locked Column Box/Box: r279c7|r1279c9 => r56c7<>8,r5c9<>8Locked Column Box/Box: r39c7|r139c9 => r6c7<>5Naked Row Pair: r5c18 => r5c26<>8UR+2rd (36): r89c34 => r9c3<>3+-------------------+------------------+-----------------+|   58    89     7  |   26    26    1  |    4    3  589  ||    4    18   128  |    5     3    9  |   78    6  278  ||  256     3   269  |    8     7    4  |   59    1  259  |+-------------------+------------------+-----------------+|  238  6789  2389  | 2679  2568  678  |    1  258    4  ||   28   679     5  |    1     4   67  |  379   28  379  ||  128  1789     4  |  279   258    3  |   79  258    6  |+-------------------+------------------+-----------------+| 1368     2  1368  |    4     9    5  |  368    7   38  ||    9     5    36* |  367*   68  678  |    2    4    1  ||    7     4   368- |   36*    1    2  | 3568    9  358  |+-------------------+------------------+-----------------+A=1 cell ALS xz-rule: r3c7-9-r179c9 => r3c9<>5A=1 cell ALS xz-rule: r3c9-9-r23789c3 => r3c1<>2Locked Column Line/Box: r23c3 => r4c3<>2A=1 cell ALS xz-rule: r3c1-5-r23567c7 => r7c1<>6Locked Column Line/Box: r13c9 => r5c9<>9UR+3C/2SL (68): r79c37 => r7c73<>8+------------------+------------------+----------------+|   5    89     7  |   26    26    1  |   4    3   89  ||   4    18   128  |    5     3    9  |  78    6  278  ||   6     3    29  |    8     7    4  |   5    1   29  |+------------------+------------------+----------------+| 238  6789   389  | 2679  2568  678  |   1  258    4  ||  28   679     5  |    1     4   67  | 379   28   37  || 128  1789     4  |  279   258    3  |  79  258    6  |+------------------+------------------+----------------+| 138     2  1368- |    4     9    5  | 368-   7   38  ||   9     5    36  |  367    68  678  |   2    4    1  ||   7     4    68* |   36     1    2  | 368*   9    5  |+------------------+------------------+----------------+A=1 cell ALS xz-mer: r5c6-67-r4c134568 => r6c4<>7,r4c2<>8,r4c2<>9UR+2rd (67): r45c26 => r4c6<>6+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+| 238    67* 389  | 2679  2568  678- |   1  258    4  ||  28   679*   5  |    1     4   67* | 379   28   37  || 128  1789    4  |   29   258    3  |  79  258    6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+3U/2SL (79): r56c27 => r5c7<>7+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+| 238    67  389  | 2679  2568   78  |   1  258    4  ||  28   679*   5  |    1     4   67  | 379-  28   37  || 128  1789*   4  |   29   258    3  |  79* 258    6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+2KX (28): r45c18, r6c12478 => r4c1<>8+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+| 238-   67  389  | 2679  2568   78  |   1  258*   4  ||  28*  679    5  |    1     4   67  |  39   28*  37  || 128# 1789#   4  |   29#  258    3  |  79# 258#   6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+4X/2SL (58): r46c58, r46c4|r45c6 => r4c8<>8+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+|  23    67  389  | 2679# 2568*  78# |   1  258-   4  ||  28   679    5  |    1     4   67# |  39   28   37  || 128  1789    4  |   29#  258*   3  |  79  258*   6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+2kx (28): r56c18, r4c8 => r6c1<>2+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+|  23    67  389  | 2679  2568   78  |   1   25#   4  ||  28*  679    5  |    1     4   67  |  39   28*  37  || 128- 1789    4  |   29   258    3  |  79  258*   6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+3C/2SL (25): r46c58 => r6c5<>2+-----------------+------------------+----------------+|   5    89    7  |   26    26    1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+|  23    67  389  | 2679  2568*  78  |   1   25*   4  ||  28   679    5  |    1     4   67  |  39   28   37  ||  18  1789    4  |   29   258-   3  |  79  258*   6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+UR+2B/1SL (26): r14c45 => r4c4<>6+-----------------+------------------+----------------+|   5    89    7  |   26*   26*   1  |   4    3   89  ||   4    18  128  |    5     3    9  |  78    6  278  ||   6     3   29  |    8     7    4  |   5    1   29  |+-----------------+------------------+----------------+|  23    67  389  | 2679- 2568*  78  |   1   25    4  ||  28   679    5  |    1     4   67  |  39   28   37  ||  18  1789    4  |   29    58    3  |  79  258    6  |+-----------------+------------------+----------------+| 138     2  136  |    4     9    5  |  36    7   38  ||   9     5   36  |  367    68  678  |   2    4    1  ||   7     4   68  |   36     1    2  | 368    9    5  |+-----------------+------------------+----------------+Advanced 3-line BUG Lite (XY:r8c5|r5c6-6-r8c6, SL:r4c2=6=r5c2): r4c256|r8c56|r5c26 => r4c5<>6,r8c6<>6,r5c2<>65-node XY-chain (r1c2-9-r5c2-7-r5c9-3-r7c9-8-) => r1c9<>8The Solution is completed with singles `
Mike Barker

Posts: 458
Joined: 22 January 2006

New arrival ~
.......4.89.2..5...2..35..9..1.7.6...4...6..7..8.1.3...1..54..325.9..4.........7.
54..6..239.3...4.7......6......37...3..2.6..1...48......2......7.5...3.261..2..95
Eioru

Posts: 182
Joined: 16 August 2006

A new puzzle with 3 Unique Retangle ( 2xtype1 + 1xtype4 ) and 1 APE more!
Code: Select all
`..6....9551....7....2..7.....34....19..2.......1..54..7..8..53....3.....8...49...`
Eioru

Posts: 182
Joined: 16 August 2006

Eioru wrote:A new puzzle with 3 Unique Retangle ( 2xtype1 + 1xtype4 ) and 1 APE more!

Code: Select all
` *-------------------------------------------------------------* | 34     7      6  | 1      238    2348 | 238    9      5     | | 5      1      8  | 69     2369   2346 | 7      246    2346  | | 34     9      2  | 5      368    7    | 1368   1468   3468  | |------------------+--------------------+---------------------| | 26     5      3  | 4      6789   68   | 2689   2678   1     | | 9      4      7  | 2      1368   1368 | 368    5      368   | | 26     8      1  | 69     3679   5    | 4      267    23679 | |------------------+--------------------+---------------------| | 7      26     49 | 8      126    126  | 5      3      49    | | 1      26     49 | 3      5      26   | 89     478    4789  | | 8      3      5  | 7      4      9    | 126    126    26    | *-------------------------------------------------------------*`

[r6c9]=3=[r6c5](-3-[r3c5])=7=[r4c5]=9=[r4c7]-9-[r8c7]-8-[r1c7]=
=8=[r1c56]-8-[(r3c5)]-6-[r2c4]=6=[r6c4],

and so r6c9 must be "3" which solves the puzzle.
Another interesting (although useless) deduction in this puzzle is the following:

Suppose that r5c79 are not "6". Then:

-6-[r5c79]-3,8-[r5c56]=3,8|2=[r7c5](-2-[r8c6])-2-[r57c6]-6-[r8c6],

and so r5c7 or r5c9 must be "6".

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Eioru wrote:A new puzzle with 3 Unique Retangle ( 2xtype1 + 1xtype4 ) and 1 APE more!
Code: Select all
`..6....9551....7....2..7.....34....19..2.......1..54..7..8..53....3.....8...49...`

Code: Select all
`# after Singles, Naked Pair, Naked Triple, and 2x UR Type 1 ... # ... no sign of a UR Type 4 *--------------------------------------------------------------------* | 34     7      6      | 1      238    2348   | 238    9      5      | | 5      1      8      | 69     2369   2346   | 7      246    2346   | | 34     9      2      | 5      368    7      | 1368   1468   3468   | |----------------------+----------------------+----------------------| | 26     5      3      | 4      6789   68     | 2689   2678   1      | | 9      4      7      | 2      1      368    | 368    5      368    | | 26     8      1      | 69     3679   5      | 4      267    23679  | |----------------------+----------------------+----------------------| | 7      26     49     | 8      26     1      | 5      3      49     | | 1      26     49     | 3      5      26     | 89     478    78     | | 8      3      5      | 7      4      9      | 126    126    26     | *--------------------------------------------------------------------*`

Code: Select all
`# after DIC, Naked Triple, and Locked Candidates (1), still no UR Type 4# I don't do APE, so maybe it's exposed after that# however, [r1c5]<>2 (from Singles Forcing Net) => solution *--------------------------------------------------------------------* | 34     7      6      | 1      28     234    | 238    9      5      | | 5      1      8      | 69     39     2346   | 7      246    2346   | | 34     9      2      | 5      68     7      | 1368   1468   3468   | |----------------------+----------------------+----------------------| | 26     5      3      | 4      79     68     | 2689   2678   1      | | 9      4      7      | 2      1      368    | 368    5      368    | | 26     8      1      | 69     379    5      | 4      267    23679  | |----------------------+----------------------+----------------------| | 7      26     49     | 8      26     1      | 5      3      49     | | 1      26     49     | 3      5      26     | 89     478    78     | | 8      3      5      | 7      4      9      | 126    126    26     | *--------------------------------------------------------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

This one has 6 x Turbot Fish and 6 x Bidirectional Cycle.

Code: Select all
`3...7...9.4...2.1....8.......7..4...2...3...8.1.6..2.......1....5.2...8.9...8...3`

And breaking the record of Bidirectional Cycle.
Eioru

Posts: 182
Joined: 16 August 2006

Ocean wrote:Here is one of the highest counts of forcing chains I could find. The 'dynamic' chains add to 49. Don't know how many of them that are really 'needed', but the numbers come from Explainer.
Code: Select all
` *-----------* |...|..1|..2| |.3.|.2.|.4.| |5..|6..|...| |---+---+---| |..6|...|..7| |.7.|.1.|.3.| |8..|...|5..| |---+---+---| |7..|..5|...| |...|.3.|.2.| |..9|8..|6..| *-----------*`

#
Analysis results
Difficulty rating: 9,2 / 10
This Sudoku can be solved using the following logical methods:
...
27 x Dynamic Region Forcing Chains
17 x Dynamic Contradiction Forcing Chains
4 x Dynamic Cell Forcing Chains
1 x Dynamic Double Forcing Chains
#

The set of 32 puzzles recently published in the 'hardest sudokus' thread contains one puzzle with 33 x Dynamic Contradiction Forcing Chains. Another of those puzzles contains 54 x 'dynamic' forcing chains (when the various types are added). The counts given by Sudoku Explainer's analysis is only an indication of how many chains that are "needed", since the numbers may change when the order of application is altered (typically the case for permuted versions of the same puzzle).

Here is a puzzle with 75 'dynamic' chains (Thanks to m_b_metcalf) :

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` 1 . . | 2 . . | 3 . . . 4 . | . 5 . | . 6 . . . . | . . 7 | . . .-------+-------+------- 3 . . | 7 . . | 8 . . . 9 . | . 4 . | . 5 . . . . | . . . | . . .-------+-------+------- 8 . . | 3 . . | 1 . . . 5 . | . 6 . | . 9 . . . . | . . . | . . .`

#
Analysis results
Difficulty rating: 9,6
This Sudoku can be solved using the following logical methods:
58 x Hidden Single
1 x Direct Hidden Pair
1 x Naked Single
1 x Direct Hidden Triplet
4 x Pointing
2 x Naked Pair
7 x Hidden Pair
4 x Swordfish
3 x XY-Wing
1 x Forcing X-Chain
3 x Bidirectional Cycle
6 x Forcing Chain
6 x Region Forcing Chains
5 x Dynamic Cell Forcing Chains
15 x Dynamic Contradiction Forcing Chains
3 x Dynamic Double Forcing Chains
52 x Dynamic Region Forcing Chains
#

JPF
JPF
2017 Supporter

Posts: 3861
Joined: 06 December 2005
Location: Paris, France

Still with Sudoku Explainer, here is a puzzle with 30 Nishio Forcing Chains :

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` . . . | . . . | . . . . . 1 | 2 . 3 | 4 . . . 5 6 | 4 . 7 | 2 1 .-------+-------+------- . 7 3 | . . . | 1 6 . . . . | . 1 . | . . . . 1 2 | . . . | 5 4 .-------+-------+------- . 3 8 | 1 . 5 | 6 2 . . . 5 | 3 . 4 | 7 . . . . . | . . . | . . .`
#
Analysis results
Difficulty rating: 9,2
This Sudoku can be solved using the following logical methods:
50 x Hidden Single
2 x Direct Hidden Pair
3 x Pointing
1 x X-Wing
1 x Bidirectional X-Cycle
1 x Forcing Chain
30 x Nishio Forcing Chains
2 x Cell Forcing Chains
1 x Dynamic Cell Forcing Chains
3 x Dynamic Contradiction Forcing Chains
#

JPF
JPF
2017 Supporter

Posts: 3861
Joined: 06 December 2005
Location: Paris, France

There's something fishy about that result. It may be 9.2, but nothing a good fisherman (or at least fisherprgram) can't handle with a little help from a few grouped nice loops:
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`Locked Column Line/Box: r45c4 => r1c4<>5Locked Column Line/Box: r56c4 => r9c4<>7Locked Column Line/Box: r45c6 => r9c6<>2Row Finned Franken Jellyfish: r37c159|r46c1469 => r5c46<>9,r12589c1<>9,r12589c9<>9,r1289c5<>9+---------------------+------------------------+----------------------+| 23478-9  2489  479  |    689   568-9      1  | 389  35789  35678-9  ||    78-9    89    1  |      2   568-9      3  |   4   5789   5678-9  ||     389*    5    6  |      4      89*     7  |   2      1      389* |+---------------------+------------------------+----------------------+|     589*    7    3  |    589*      4    289* |   1      6      289* ||  4568-9  4689   49  | 5678-9       1  268-9  | 389   3789   2378-9  ||     689*    1    2  |   6789*      3    689* |   5      4      789* |+---------------------+------------------------+----------------------+|     479*    3    8  |      1      79*     5  |   6      2       49* ||   126-9   269    5  |      3   268-9      4  |   7     89     18-9  || 12467-9  2469  479  |    689  2678-9    689  | 389   3589  13458-9  |+---------------------+------------------------+----------------------+Row X-Wing: r28c28 => r159c2<>9,r159c8<>9+--------------------+------------------+---------------------+| 23478  248-9  479  |  689   568    1  | 389  3578-9  35678  ||    78     89*   1  |    2   568    3  |   4    5789*  5678  ||   389      5    6  |    4    89    7  |   2       1    389  |+--------------------+------------------+---------------------+|   589      7    3  |  589     4  289  |   1       6    289  ||  4568  468-9   49  | 5678     1  268  | 389   378-9   2378  ||   689      1    2  | 6789     3  689  |   5       4    789  |+--------------------+------------------+---------------------+|   479      3    8  |    1    79    5  |   6       2     49  ||   126    269*   5  |    3   268    4  |   7      89*    18  || 12467  246-9  479  |  689  2678  689  | 389   358-9  13458  |+--------------------+------------------+---------------------+B=4 cell ALS xy-rule: r2c128 -5- r9c4678 -6- r3789c5 => r2c5<>84-element Strong Nice Loop: r2c1 -7- r7c1 =7= r7c5 =9= r3c5 =8= r1c45 ~8~  => r1c12<>84-element Nice Loop: r2c2 -8- r2c1 -7- r7c1 =7= r7c5 =9= r3c5 ~9~  => r3c1<>93-element Advanced Colouring: r5c2 =8= r2c2 =9= r1c3 -9- r5c3 =9= r5c7 ~8~ r5c2 => r5c7<>8Column Finless Franken Swordfish: r14569c4|r4569c6|r19c7 => r1c589<>8,r9c589<>8+------------------+-------------------+---------------------+|  2347   24  479  |  689*  56-8    1  | 389* 357-8  3567-8  ||    78   89    1  |    2     56    3  |   4   5789    5678  ||    38    5    6  |    4     89    7  |   2      1     389  |+------------------+-------------------+---------------------+|   589    7    3  |  589*     4  289* |   1      6     289  ||  4568  468   49  | 5678*     1  268* |  39    378    2378  ||   689    1    2  | 6789*     3  689* |   5      4     789  |+------------------+-------------------+---------------------+|   479    3    8  |    1     79    5  |   6      2      49  ||   126  269    5  |    3    268    4  |   7     89      18  || 12467  246  479  |  689* 267-8  689* | 389*  35-8  1345-8  |+------------------+-------------------+---------------------+Locked Column Line/Box Pair: r12c5 => r89c5<>6Locked Row Line/Box: r9c46 => r9c12<>6Naked Column Pair: r19c2 => r5c2<>4,r8c2<>2XY-wing => r5c8<>8Hidden Column Pair: r28c8 => r2c8=89Naked Row Pair: r2c28 => r2c19<>8The Solution is completed`
Mike Barker

Posts: 458
Joined: 22 January 2006

JPF wrote:here is a puzzle with 30 Nishio Forcing Chains

Is a high Nishio chain count meaningful?

At the outset, the two fish (9)r3467\c159b5 and (9)c3467\r159b5 yield 24 eliminations. Specifically ...
Code: Select all
`        before                        after 9 9 9 | 9 9 9 | 9 9 9        . . 9 | 9 . 9 | 9 . . 9 9 . | . 9 . | . 9 9        . 9 . | . . . | . 9 . 9 . . | . 9 . | . . 9        9 . . | . 9 . | . . 9-------+-------+-------      -------+-------+------- 9 . . | 9 9 9 | . . 9        9 . . | 9 . 9 | . . 9 9 9 9 | 9 . 9 | 9 9 9        . . 9 | . . . | 9 . . 9 . . | 9 9 9 | . . 9        9 . . | 9 . 9 | . . 9-------+-------+-------      -------+-------+------- 9 . . | . 9 . | . . 9        9 . . | . 9 . | . . 9 9 9 . | . 9 . | . 9 9        . 9 . | . . . | . 9 . 9 9 9 | 9 9 9 | 9 9 9        . . 9 | 9 . 9 | 9 . .`

If none of these eliminations resulted from a technique of lower difficulty rating, I believe Sudoku Explainer would count 24 Nishio chains.

Note: These same fish, likely for the same puzzle, have been posted somewhere in this forum before.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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