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by **P.O.** » Fri May 05, 2023 5:43 pm

Code: Select all: . 4 3 . 1 2 . 5 . 2 . 5 . . . . . 1 7 9 1 . 4 . . 6 . . . 6 . . 4 5 . . 5 2 . . 8 3 . 1 . . . . 2 . . . . 7 . . . 4 . . . 8 6 . . 2 . 3 . . 7 . 1 . . . . 9 3 . . .43.12.5.2.5.....1791.4..6...6..45..52..83.1....2....7...4...86..2.3..7.1....93.. 68 4 3 6789 1 2 789 5 89 2 68 5 36789 679 678 4789 349 1 7 9 1 358 4 58 28 6 238 389 1378 6 179 79 4 5 239 2389 5 2 479 679 8 3 469 1 49 3489 138 489 2 569 156 4689 349 7 39 357 79 4 257 157 129 8 6 4689 568 2 1568 3 1568 149 7 459 1 5678 478 5678 2567 9 3 24 245

by **SteveG48** » Fri May 05, 2023 7:08 pm

Code: Select all: *----------------------------------------------------------------------* | 68 4 3 | 6789 1 2 |d789 5 b8-9 | | 2 68 5 | 36789 679 678 |d4789 c349 1 | | 7 9 1 |f358 4 deg58 |d28 6 c238 | *-----------------------+----------------------+-----------------------| | 389 1378 6 | 179 79 4 | 5 239 a2389 | | 5 2 479 | 679 8 3 | 469 1 abk49 | |fg3489 138 fg489 | 2 569 156 |e4689 de349 7 | *-----------------------+----------------------+-----------------------| | h39 i357 79 | 4 i257 h157 |j129 8 6 | | 4689 568 2 | 1568 3 1568 | 149 7 abk459 | | 1 5678 478 | 5678 2567 9 | 3 c24 bk245 | *----------------------------------------------------------------------*

by **P.O.** » Sun May 07, 2023 5:58 pm

thank you for your answer, i also solve the puzzle by eliminating n9 from r1c9 with two methods, first a rather complicated forcing-chain built on the first resolution state, and a second by developing the two terms of an OR relation proving in each of their context much more simply the contradiction of n9r1c9
first method:

Code: Select all: 9r1c9 => r6c1 <> 3,4,8,9 r1c9=9 - r5c9{n9 n4} - 25r89c9 - r9c8{n2 n4} - r2c8{n49 n3} - r3n3{c9 c4} - c4n5{r3 r89} - r7n5{c56 c2} - r7n3{c2 c1} r1c9=9 - r5c9{n9 n4} - 25r89c9 - r9c8{n2 n4} - b7n4{r9c3 r8c1} r1c9=9 - r5c9{n9 n4} - 25r89c9 - r9c8{n2 n4} - r2c8{n49 n3} - r3c9{n23 n8} - b6n8{r4c9 r6c7} r1c9=9 - r5c9{n9 n4} - 25r89c9 - r9c8{n2 n4} - r2c8{n49 n3} - r6c8{n34 n9} => r1c9 <> 9 ste.

second method:
n2r4c8 OR n2r4c9 => r1c9 <> 9
ste.
n2r4c8 context:

Hidden Text: Show

Code: Select all: ((2 0) (4 8 6) (2 3 9)) n2r4c8 ((4 1 9) (9 8 9) (2 4)) n4r9c8 ((4 1 9) (9 8 9) (2 4)) n4r9c8 ((4 2 7) (5 9 6) (4 9)) n4r5c9 ((4 2 1) (8 1 7) (4 6 8 9)) n4r8c1 ((4 2 1) (2 7 3) (4 7 8 9)) n4r2c7 ((4 2 2 2) ((5 3 4) (4 7 9)) ((6 3 4) (4 8 9))) n4r56c3 ((4 2 7) (5 9 6) (4 9)) n4r5c9 ((4 3 7) (2 7 3) (4 7 8 9)) n4r2c7 ((4 3 1 2) ((6 1 4) (3 4 8 9)) ((6 3 4) (4 8 9))) n4r6c13 ((4 2 1) (8 1 7) (4 6 8 9)) n4r8c1 ((6 3 10) (1 1 1) (6 8)) n6r1c1 ((9 3 1 11) ((8 7 9) (1 4 9)) ((8 9 9) (4 5 9))) n9r8c79 ((9 3 1 11) ((7 1 7) (3 9)) ((7 3 7) (7 9))) n9r7c13 ((6 3 2 11) ((8 2 7) (5 6 8)) ((9 2 7) (5 6 7 8))) n6r89c2 ((4 2 1) (2 7 3) (4 7 8 9)) n4r2c7 ((7 3 10) (1 7 3) (7 8 9)) n7r1c7 ((7 3 1 11) ((2 4 2) (3 6 7 8 9)) ((2 5 2) (6 7 9)) ((2 6 2) (6 7 8))) n7r2c456 ((4 3 1 2) ((6 1 4) (3 4 8 9)) ((6 3 4) (4 8 9))) n4r6c13

Code: Select all: 6 4 3 89 1 2 7 5 89 2 8 5 3679 679 67 4 39 1 7 9 1 358 4 58 28 6 238 389 137 6 179 79 4 5 2 389 5 2 79 679 8 3 69 1 4 389 13 489 2 569 156 689 39 7 39 357 79 4 257 157 12 8 6 4 56 2 1568 3 1568 19 7 59 1 567 78 5678 2567 9 3 4 25 9r1c9 => r678c6 <> 1 r1c9=9 - c8n9{r2 r6} - r5c7{n9 n6} - r6c7{n69 n8} - 13r6c12 r1c9=9 - 25r89c9 - r7c7{n2 n1} r1c9=9 - r1c4{n9 n8} - c6n8{r3 r8} => r1c9 <> 9

n2r4c9 context:

Hidden Text: Show

Code: Select all: ((2 0) (4 9 6) (2 3 8 9)) n2r4c9 ((8 1 10) (6 7 6) (4 6 8 9)) n8r6c7 ((3 1 10) (3 9 3) (2 3 8)) n3r3c9 ((2 1 1) (3 7 3) (2 8)) n2r3c7 ((8 1 2 11) ((1 9 3) (8 9)) ((3 9 3) (2 3 8))) n8r13c9 ((8 1 1 11) ((4 1 4) (3 8 9)) ((4 2 4) (1 3 7 8))) n8r4c12 ((3 1 2 11) ((4 8 6) (2 3 9)) ((6 8 6) (3 4 9))) n3r46c8 ((8 1 10) (6 7 6) (4 6 8 9)) n8r6c7 ((6 2 10) (5 7 6) (4 6 9)) n6r5c7 ((2 2 9) (3 7 3) (2 8)) n2r3c7 ((8 2 1) (9 3 7) (4 7 8)) n8r9c3 ((6 2 1 11) ((6 5 5) (5 6 9)) ((6 6 5) (1 5 6))) n6r6c56 ((8 2 2 2) ((1 9 3) (8 9)) ((3 9 3) (2 3 8))) n8r13c9 ((8 2 1 2) ((4 1 4) (3 8 9)) ((4 2 4) (1 3 7 8))) n8r4c12 ((3 1 10) (3 9 3) (2 3 8)) n3r3c9 ((3 2 1) (2 4 2) (3 6 7 8 9)) n3r2c4 ((8 2 1 31) ((3 4 2) (3 5 8)) ((3 6 2) (5 8))) n8r3c46 ((5 2 1 31) ((3 4 2) (3 5 8)) ((3 6 2) (5 8))) n5r3c46 ((3 2 2 2) ((4 8 6) (2 3 9)) ((6 8 6) (3 4 9))) n3r46c8 ((2 1 1) (3 7 3) (2 8)) n2r3c7 ((2 2 1) (9 8 9) (2 4)) n2r9c8 ((2 2 1) (7 5 8) (2 5 7)) n2r7c5 ((2 2 1) (9 8 9) (2 4)) n2r9c8 ((2 3 1) (7 5 8) (2 5 7)) n2r7c5 ((6 2 10) (5 7 6) (4 6 9)) n6r5c7 ((6 3 1 2) ((6 5 5) (5 6 9)) ((6 6 5) (1 5 6))) n6r6c56 ((8 2 1) (9 3 7) (4 7 8)) n8r9c3 ((4 3 10) (8 1 7) (4 6 8 9)) n4r8c1 ((4 3 1 11) ((9 8 9) (2 4)) ((9 9 9) (2 4 5))) n4r9c89 ((4 3 2 11) ((5 3 4) (4 7 9)) ((6 3 4) (4 8 9))) n4r56c3 ((8 3 1 2) ((8 4 8) (1 5 6 8)) ((8 6 8) (1 5 6 8))) n8r8c46 ((8 2 1 31) ((3 4 2) (3 5 8)) ((3 6 2) (5 8))) n8r3c46 ((2 3 20) (3 7 3) (2 8)) n2r3c7

Code: Select all: 68 4 3 679 1 2 79 5 89 2 68 5 3 679 67 479 49 1 7 9 1 58 4 58 2 6 3 389 1378 6 179 79 4 5 39 2 5 2 479 79 8 3 6 1 49 39 13 49 2 569 156 8 349 7 39 357 79 4 2 157 19 8 6 4 56 2 1568 3 1568 19 7 59 1 567 8 567 567 9 3 2 45 9r1c9 => r9c9 <> 4,5 r1c9=9 - r5c9{n9 n4} r1c9=9 - r8c9{n9 n5} => r1c9 <> 9

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Puzzle 133

Puzzle 133

Re: Puzzle 133

Re: Puzzle 133