The New Sudoku Players' Forum

by **Carcul** » Mon Sep 25, 2006 2:52 pm

Thanks Ravel for your explanation.
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

by **gsf** » Mon Sep 25, 2006 3:56 pm

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...........

by **gsf** » Mon Sep 25, 2006 4:08 pm

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

by **maria45** » Mon Sep 25, 2006 6:05 pm

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..7 3.....5.. .4..7..2. ..1..5..4 6..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

by **maria45** » Mon Sep 25, 2006 6:26 pm

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

by **Mike Barker** » Mon Sep 25, 2006 6:57 pm

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<>2 Locked Row Line/Box: r8c56 => r8c3<>8 Locked Row Line/Box: r5c79 => r5c1<>3 Locked Column Line/Box: r23c9 => r5c9<>2 Locked Column Box/Box: r37c1|r3789c3 => r45c1<>6,r4c3<>6 Locked Column Box/Box: r279c7|r1279c9 => r56c7<>8,r5c9<>8 Locked Column Box/Box: r39c7|r139c9 => r6c7<>5 Naked Row Pair: r5c18 => r5c26<>8 UR+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<>5 A=1 cell ALS xz-rule: r3c9-9-r23789c3 => r3c1<>2 Locked Column Line/Box: r23c3 => r4c3<>2 A=1 cell ALS xz-rule: r3c1-5-r23567c7 => r7c1<>6 Locked Column Line/Box: r13c9 => r5c9<>9 UR+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<>9 UR+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<>6 5-node XY-chain (r1c2-9-r5c2-7-r5c9-3-r7c9-8-) => r1c9<>8 The Solution is completed with singles

by **Eioru** » Tue Sep 26, 2006 5:46 pm

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

by **Eioru** » Fri Oct 13, 2006 8:21 am

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

Code: Select all: ..6....95 51....7.. ..2..7... ..34....1 9..2..... ..1..54.. 7..8..53. ...3..... 8...49...

by **Carcul** » Fri Oct 13, 2006 9:09 am

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

by **daj95376** » Fri Oct 13, 2006 5:21 pm

Eioru wrote:A new puzzle with 3 Unique Retangle ( 2xtype1 + 1xtype4 ) and 1 APE more!
Code: Select all
..6....95 51....7.. ..2..7... ..34....1 9..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 | *--------------------------------------------------------------------*

by **Eioru** » Fri Mar 02, 2007 4:48 pm

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.

by **JPF** » Sat Feb 23, 2008 10:09 pm

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) :

Code: Select all: 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

by **JPF** » Sun Mar 16, 2008 12:33 am

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

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

by **Mike Barker** » Sun Mar 16, 2008 4:27 am

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:

Code: Select all: Locked Column Line/Box: r45c4 => r1c4<>5 Locked Column Line/Box: r56c4 => r9c4<>7 Locked Column Line/Box: r45c6 => r9c6<>2 Row 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<>8 4-element Strong Nice Loop: r2c1 -7- r7c1 =7= r7c5 =9= r3c5 =8= r1c45 ~8~ => r1c12<>8 4-element Nice Loop: r2c2 -8- r2c1 -7- r7c1 =7= r7c5 =9= r3c5 ~9~ => r3c1<>9 3-element Advanced Colouring: r5c2 =8= r2c2 =9= r1c3 -9- r5c3 =9= r5c7 ~8~ r5c2 => r5c7<>8 Column 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<>6 Locked Row Line/Box: r9c46 => r9c12<>6 Naked Column Pair: r19c2 => r5c2<>4,r8c2<>2 XY-wing => r5c8<>8 Hidden Column Pair: r28c8 => r2c8=89 Naked Row Pair: r2c28 => r2c19<>8 The Solution is completed

by **ronk** » Sun Mar 16, 2008 12:50 pm

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.

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