The New Sudoku Players' Forum

Website · by **denis_berthier** » Wed Sep 28, 2022 11:32 am

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Code: Select all: +-------+-------+-------+ ! . . . ! 4 5 6 ! . 8 . ! ! . . . ! . . . ! 1 3 . ! ! . . . ! . . . ! . . 6 ! +-------+-------+-------+ ! 2 . 8 ! 9 . 5 ! . . 4 ! ! . . 4 ! . 6 2 ! . . 8 ! ! . . . ! 8 4 . ! . . . ! +-------+-------+-------+ ! . . 2 ! . . . ! . . . ! ! 8 . . ! . . . ! 9 2 . ! ! 9 . 5 ! 6 2 . ! . . . ! +-------+-------+-------+ ...456.8.......13.........62.89.5..4..4.62..8...84......2......8.....92.9.562....;1046;29895

WARNING: this may be a very difficult one.

by **yzfwsf** » Wed Sep 28, 2022 1:13 pm

The automatic solution path of my solver is as follows:

Hidden Text: Show

by **totuan** » Wed Sep 28, 2022 4:14 pm

Code: Select all: *--------------------------------------------------------------------------------------* | 137 12379 1379 | 4 5 6 | 27 8 279 | |&4567 &2456789 679 | 27 789 789 | 1 3 &2579 | |#57 28-579 #79 | 123-7 138-79 138-79 | 245-7 #4579 6 | |----------------------------+----------------------------+----------------------------| | 2 1367 8 | 9 137 5 | 367 167 4 | | 1357 13579 4 | 137 6 2 | 357 1579 8 | | 13567 135679 13679 | 8 4 137 | 23567 15679 123579 | |----------------------------+----------------------------+----------------------------| | 1347 1347 2 | 1357 13789 134789 | 345678 14567 *1357 | | 8 13467 1367 | 1357 137 1347 | 9 2 *1357 | | 9 1347 5 | 6 2 13478 | 3478 *147 *137 | *--------------------------------------------------------------------------------------*

My path for this one:
01: (579=4)r3c138-(4=1357)r789c89-(5)r2c9=r2c12-(5=79)r3c13 => r3c2<>579, r3c456<>79, r3c7<>7, some singles

Code: Select all: *-----------------------------------------------------------------------------* | 137 12379 1379 | 4 5 6 | 27 8 c279 | | 45 2458 6 | 27 789 789 | 1 3 25 | | 57 28 a79 | 123 138 138 | 45 b4579 6 | |-------------------------+-------------------------+-------------------------| | 2 137 8 | 9 137 5 | 367 167 4 | | 1357 13579 4 | 137 6 2 | 357 1579 8 | | 6 13579 137-9 | 8 4 137 | 2357 1579 d123579 | |-------------------------+-------------------------+-------------------------| | 1347 1347 2 | 1357 13789 13789 | 345678 14567 1357 | | 8 6 137 | 1357 137 4 | 9 2 1357 | | 9 1347 5 | 6 2 1378 | 3478 147 137 | *-----------------------------------------------------------------------------*

02: (9)r3c3=r3c9-r1c9=r6c9 => r6c3<>9

Code: Select all: *-----------------------------------------------------------------------------* | 137 1237 1379 | 4 5 6 | 27 8 279 | |&45 &2458 6 | 27 789 789 | 1 3 2-5 | |&57 28 79 | 123 138 138 | 45 4579 6 | |-------------------------+-------------------------+-------------------------| | 2 137 8 | 9 137 5 | 367 167 4 | |#1357 13579 4 | 137 6 2 | 357 1579 8 | | 6 13579 137 | 8 4 137 | 2357 1579 123579 | |-------------------------+-------------------------+-------------------------| |#1347 1347 2 |#1357 13789 13789 |$345678 $14567 *1357 | | 8 6 137 | 1357 137 4 | 9 2 *1357 | | 9 #1347 5 | 6 2 #1378 |$3478 *147 *137 | *-----------------------------------------------------------------------------*

Tridagon (137)B4578 => (5)r5c1=(4)r7c1=(4)r9c2=(5)r7c4=(8)r9c6
03: Present as diagram: r2c9<>5, some singles

Code: Select all: (45)r57c1-(45)r23c1=(5)r2c12* || (4)r9c2-(4=1357)r789c89* || (5)r7c4-r7c789=r8c9* || (8)r9c6-r9c7=(68-5)r7c78=r78c9*

Code: Select all: *--------------------------------------------------------------------* | 13 2 13 | 4 5 6 | 7 8 9 | | 45 45 6 | 7 89 89 | 1 3 2 | | 7 8 9 | 2 13 13 | 45 45 6 | |----------------------+----------------------+----------------------| | 2 137 8 | 9 137 5 | 36 167 4 | | 135 79 4 | 13 6 2 | 35 79 8 | | 6 13579 137 | 8 4 137 | 2 1579 1357 | |----------------------+----------------------+----------------------| | 134 1347 2 | 135 89 13789 | 34568 14567 1357 | | 8 6 137 | 135 137 4 | 9 2 1357 | | 9 1347 5 | 6 2 1378 | 348 147 137 | *--------------------------------------------------------------------*

From here the puzzle is not hard

Thanks for the puzzle!
totuan

by **DEFISE** » Wed Sep 28, 2022 4:41 pm

Box/Line: 1r1b1 => -1r3c1 -1r3c2 -1r3c3
Box/Line: 3r1b1 => -3r3c1 -3r3c2 -3r3c3
Box/Line: 4r2b1 => -4r3c1 -4r3c2
Box/Line: 6r8b7 => -6r7c1 -6r7c2

Code: Select all: |-----------------------------------------------------------------------------| | 137 12379 1379 | 4 5 6 | 27 8 279 | | 4567 2456789 679 | 27 789 789 | 1 3 2579 | | 57 25789 79 | 1237 13789 13789 | 2457 4579 6 | |-----------------------------------------------------------------------------| | 2 1367 8 | 9 137 5 | 367 167 4 | | 1357 13579 4 | 137 6 2 | 357 1579 8 | | 13567 135679 13679 | 8 4 137 | 23567 15679 123579 | |-----------------------------------------------------------------------------| | 1347 1347 2 | 1357 13789 134789 | 345678 14567 1357 | | 8 13467 1367 | 1357 137 1347 | 9 2 1357 | | 9 1347 5 | 6 2 13478 | 3478 147 137 | |-----------------------------------------------------------------------------|

Tridagon (1,3,7) in b4p249, b5p249, b7p168, b8p159,
10 guardians: 6r4c2, 5r5c1, 6r6c3, 9r6c3, 4r7c1, 6r8c3, 4r9c2, 5r7c4, 4r9c6, 8r9c6

S3-whip[6]: r3n4{c7 c8}- b3n5{r3c8 r2c9}- b9{n5r7c9 NT:137p368}- r9c9{n1 .} => -2r3c7
Naked quads: 4579r3c1378 => -5r3c2 -7r3c2 -9r3c2 -7r3c4 -7r3c5 -9r3c5 -7r3c6 -9r3c6
Box/Line: 7b2r2 => -7r2c1 -7r2c2 -7r2c3 -7r2c9
Box/Line: 9b2r2 => -9r2c2 -9r2c3 -9r2c9
Single(s): 6r2c3, 6r8c2, 4r8c6, 6r6c1
whip[2]: r3n9{c3 c8}- r5n9{c8 .} => -9r6c3
Box/Line: 9c3b1 => -9r1c2

Code: Select all: |--------------------------------------------------------------------| | 137 1237 1379 | 4 5 6 | 27 8 279 | | 45 2458 6 | 27 789 789 | 1 3 25 | | 57 28 79 | 123 138 138 | 457 4579 6 | |--------------------------------------------------------------------| | 2 137 8 | 9 137 5 | 367 167 4 | | 1357 13579 4 | 137 6 2 | 357 1579 8 | | 6 13579 137 | 8 4 137 | 2357 1579 123579 | |--------------------------------------------------------------------| | 1347 1347 2 | 1357 13789 13789 | 345678 14567 1357 | | 8 6 137 | 1357 137 4 | 9 2 1357 | | 9 1347 5 | 6 2 1378 | 3478 147 137 | |--------------------------------------------------------------------|

5 guardians remaining: 5r5c1, 4r7c1, 4r9c2, 5r7c4, 8r9c6

I consider this partial S2-whip from 5r2c9:
r8n5{c9 c4*}- r7{c4n5 HP:56c78}- c7n8{r7 r9*}- c7n4{r9 r3}- r3n5{c7 c1*}- r2c1{n5 n4*}- r7n4{c1 c2*}-
Each of the 5 guardians is seen by a right-linking candidate tagged *
=> -5r2c9
Single(s): 2r2c9, 7r1c7, 9r1c9, 7r2c4, 2r1c2, 8r3c2, 2r3c4, 9r3c3, 7r3c1, 2r6c7
Hidden pairs: 79r5c28 => -1r5c2 -3r5c2 -5r5c2 -1r5c8 -5r5c8
Hidden pairs: 89c5r27 => -1r7c5 -3r7c5 -7r7c5
whip[2]: c3n7{r8 r6}- c6n7{r6 .} => -7r8c5
Single(s): 7r4c5
Naked pairs: 13c6r36 => -1r7c6 -3r7c6 -1r9c6 -3r9c6
whip[6]: r4c2{n3 n1}- r5n1{c1 c4}- r5n3{c4 c1}- r1c1{n3 n1}- c3n1{r1 r8}- b8n1{r8c4 .} => -3r4c7
Single(s): 6r4c7, 1r4c8, 3r4c2, 6r7c8
Box/Line: 3r9b9 => -3r7c7 -3r7c9 -3r8c9
whip[3]: r5n1{c4 c1}- r1c1{n1 n3}- r7n3{c1 .} => -3r5c4
STTE

by **Cenoman** » Wed Sep 28, 2022 9:11 pm

Code: Select all: +----------------------------+--------------------------+----------------------------+ | 137 12379 1379 | 4 5 6 | d27 8 d279 | | 4567 2456789 679 | 27 789 789 | 1 3 d2579 | | 57 25789 79 | 1237 13789 13789 | a45-27 b4579 6 | +----------------------------+--------------------------+----------------------------+ | 2 1367 8 | 9 137 5 | 367 167 4 | | 1357 13579 4 | 137 6 2 | 357 1579 8 | | 13567 135679 13679 | 8 4 137 | 23567 15679 123579 | +----------------------------+--------------------------+----------------------------+ | 1347 1347 2 | 1357 13789 134789 | 345678 14567 c1357 | | 8 13467 1367 | 1357 137 1347 | 9 2 c1357 | | 9 1347 5 | 6 2 13478 | 3478 c147 c137 | +----------------------------+--------------------------+----------------------------+

At this resolution state, the TH(137)b4578 has ten guardians. Some eliminations are welcome.
1. (4)r3c7 = r3c8 - (4=1375)b9p3689 - (5=927)b3p136 => -27 r3c7; lcls, 4 placements (six guardians remain)

Code: Select all: +------------------------+-------------------------+----------------------------+ | 137 12379 1379 | 4 5 6 | 27 8 279^ | | a45 2458 6 | 27 789 789 | 1 3 2-5 | | b57 28 79^ | 123 138 138 | 45 c4579^ 6 | +------------------------+-------------------------+----------------------------+ | 2 137* 8 | 9 137* 5 | 367 167 4 | | a1357* 13579 4 | 137* 6 2 | 357 1579 8 | | 6 13579 137-9* | 8 4 137* | 2357 1579 123579^ | +------------------------+-------------------------+----------------------------+ | a1347* 1347 2 | x1357* 13789 13789 | 345678 14567 B1357 | | 8 6 137* | y1357 137* 4 | 9 2 zB1357 | | 9 A1347* 5 | 6 2 A1378* | B3478 B147 B137 | +------------------------+-------------------------+----------------------------+

2. Kite: (9)r6c9 = r1c9 - r3c8 = r3c3 => -9 r6c3
3.TH(137)b4578 having five guardians:
(45)r257c1 - r3c1 = (5)r3c78
(4)r9c2|(8)r9c6 - (48=1375)b9p36789
(5)r7c4 - r8c4 = (5)r8c9
=> -5 r2c9; lcls, 10 placements

Code: Select all: +----------------------+----------------------+-------------------------+ | 13 2 13 | 4 5 6 | 7 8 9 | | 45 45 6 | 7 89* 89* | 1 3 2 | | 7 8 9 | 2 13 13 | 45 45 6 | +----------------------+----------------------+-------------------------+ | 2 137 8 | 9 137 5 | 36 167 4 | | 135 79 4 | 13 6 2 | 35 79 8 | | 6 13579 137 | 8 4 137 | 2 1579 1357 | +----------------------+----------------------+-------------------------+ | 134 1347 2 | 135 89* 13789* | 34568 14567 1357 | | 8 6 137 | 135 137 4 | 9 2 1357 | | 9 1347 5 | 6 2 137+8 | 348 147 137 | +----------------------+----------------------+-------------------------+

4. UR(89)r37c56 using single external => +8 r9c6; lcls, 7 placements

Code: Select all: +---------------------+--------------------+--------------------+ | 13 2 13 | 4 5 6 | 7 8 9 | | 45 45 6 | 7 8 9 | 1 3 2 | | 7 8 9 | 2 13 13 | 45 45 6 | +---------------------+--------------------+--------------------+ | 2 13-7 8 | 9 137* 5 | 6 17 4 | | 135 79 4 | 13 6 2 | 35 79 8 | | 6 59 137* | 8 4 13-7 | 2 59 137 | +---------------------+--------------------+--------------------+ | 134 1347 2 | 135 9 137 | 8 6 1357 | | 8 6 137* | 135 137* 4 | 9 2 1357 | | 9 137 5 | 6 2 8 | 34 147 137 | +---------------------+--------------------+--------------------+

5. Skyscraper: (7)r6c3 = r8c3 - r8c5 = r4c5 => -7 r4c2, r6c6; lcls, 4 placements

Code: Select all: +-----------------+------------------+------------------+ | 13 2 13 | 4 5 6 | 7 8 9 | | 45 45 6 | 7 8 9 | 1 3 2 | | 7 8 9 | 2 13 13 | 45 45 6 | +-----------------+------------------+------------------+ | 2 3 8 | 9 7 5 | 6 1 4 | | 15 79 4 | 13 6 2 | 35 79 8 | | 6 59 17 | 8 4 13 | 2 59 37 | +-----------------+------------------+------------------+ | 34 14 2 | a35+1 9 7 | 8 6 15 | | 8 6 y37 |xb15+3 b13 4 | 9 2 Ac57+1 | | 9 z17 5 | 6 2 8 | 34 47 A3+7-1 | +-----------------+------------------+------------------+

6. BUG+4
(1)r7c4 - r8c45 = (1)r8c9
(1)r8c9|(7)r9c9
(3)r8c4 - (3=7)r8c3 - (7=1)r9c2
=> -1 r9c9; ste
...or

Hidden Text: Show

Website · by **denis_berthier** » Thu Sep 29, 2022 5:35 am

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Thannks for your answers.

At first, I thought I couldn't solve this puzzle with my current set of rules.
Indeed, allowing whips[20] and all the ORk-chains of any length, what I got didn't go far:

Code: Select all: t-whip[4]: r3c1{n5 n7} - r3c3{n7 n9} - r2c3{n9 n6} - c1n6{r2 .} ==> r6c1≠5 whip[5]: r3c3{n9 n7} - r3c1{n7 n5} - r2n5{c2 c9} - b3n9{r2c9 r3c8} - r5n9{c8 .} ==> r1c2≠9 t-whip[4]: r1n9{c9 c3} - r3c3{n9 n7} - r3c1{n7 n5} - r2n5{c2 .} ==> r2c9≠9 biv-chain[3]: c9n9{r1 r6} - r6n2{c9 c7} - r1c7{n2 n7} ==> r1c9≠7 whip[5]: c1n6{r6 r2} - r2n4{c1 c2} - c2n8{r2 r3} - c2n9{r3 r5} - c2n5{r5 .} ==> r6c2≠6 whip[8]: r1c7{n7 n2} - c9n2{r2 r6} - c9n7{r6 r2} - r2c4{n7 n2} - r3n2{c4 c2} - c2n8{r3 r2} - r2n4{c2 c1} - r2n5{c1 .} ==> r7c7≠7 whip[8]: r1c7{n7 n2} - c9n2{r2 r6} - c9n7{r6 r2} - r2c4{n7 n2} - r3n2{c4 c2} - c2n8{r3 r2} - r2n4{c2 c1} - r2n5{c1 .} ==> r9c7≠7 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠1 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠3 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠7 whip[10]: c1n6{r6 r2} - r2n4{c1 c2} - c2n8{r2 r3} - c2n2{r3 r1} - r1c7{n2 n7} - r4c7{n7 n3} - r5c7{n3 n5} - c1n5{r5 r3} - c8n5{r3 r7} - r7n6{c8 .} ==> r6c7≠6 whip[10]: c1n6{r6 r2} - r2n4{c1 c2} - c2n8{r2 r3} - c2n2{r3 r1} - r1c7{n2 n7} - r4c7{n7 n3} - r5c7{n3 n5} - r6c7{n5 n2} - b3n2{r3c7 r2c9} - r2n5{c9 .} ==> r4c2≠6 whip[1]: r4n6{c8 .} ==> r6c8≠6 whip[11]: b4n5{r6c2 r5c1} - r3c1{n5 n7} - r3c3{n7 n9} - r3c8{n9 n4} - r3c7{n4 n2} - r1c7{n2 n7} - r5c7{n7 n3} - r4c7{n3 n6} - c8n6{r4 r7} - c8n5{r7 r6} - r6c7{n5 .} ==> r3c2≠5

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 137 1237 1379 ! 4 5 6 ! 27 8 29 ! ! 4567 2456789 679 ! 27 789 789 ! 1 3 257 ! ! 57 2789 79 ! 1237 13789 13789 ! 2457 4579 6 ! +-------------------------+-------------------------+-------------------------+ ! 2 137 8 ! 9 137 5 ! 367 167 4 ! ! 1357 13579 4 ! 137 6 2 ! 357 1579 8 ! ! 1367 13579 13679 ! 8 4 137 ! 2357 1579 123579 ! +-------------------------+-------------------------+-------------------------+ ! 1347 1347 2 ! 1357 89 134789 ! 34568 14567 1357 ! ! 8 13467 1367 ! 1357 137 1347 ! 9 2 1357 ! ! 9 1347 5 ! 6 2 13478 ! 348 147 137 ! +-------------------------+-------------------------+-------------------------+ OR9-anti-tridagon[12] for digits 1, 3 and 7 in blocks: b4, with cells: r4c2, r5c1, r6c3 b5, with cells: r4c5, r5c4, r6c6 b7, with cells: r9c2, r7c1, r8c3 b8, with cells: r9c6, r7c4, r8c5 with 9 guardians: n5r5c1 n6r6c3 n9r6c3 n4r7c1 n5r7c4 n6r8c3 n4r9c2 n4r9c6 n8r9c6

9 guardians is too many to deal with.

But then I thought of activating g-whips. They allow much more cleaning at the start, without going beyond length 9:

Code: Select all: Starting again from the resolution state after whips[1]: 238 g-candidates, 1262 csp-glinks and 710 non-csp glinks g-whip[3]: r1n7{c9 c123} - r3c1{n7 n5} - b3n5{r3c7 .} ==> r2c9≠7 t-whip[4]: r3c1{n5 n7} - r3c3{n7 n9} - r2c3{n9 n6} - c1n6{r2 .} ==> r6c1≠5 g-whip[4]: r1n9{c9 c123} - r3c3{n9 n7} - r3c1{n7 n5} - b3n5{r3c7 .} ==> r2c9≠9 finned-x-wing-in-columns: n9{c9 c3}{r6 r1} ==> r1c2≠9 biv-chain[3]: r2c4{n7 n2} - r2c9{n2 n5} - r8n5{c9 c4} ==> r8c4≠7 biv-chain[3]: c9n9{r1 r6} - r6n2{c9 c7} - r1c7{n2 n7} ==> r1c9≠7 z-chain[3]: c9n7{r9 r6} - r6n2{c9 c7} - r1c7{n2 .} ==> r7c7≠7, r9c7≠7 whip[5]: c1n6{r6 r2} - r2n4{c1 c2} - c2n8{r2 r3} - c2n5{r3 r5} - c2n9{r5 .} ==> r6c2≠6 g-whip[6]: r3n4{c7 c8} - b3n5{r3c8 r2c9} - c9n2{r2 r6} - c9n7{r6 r789} - r9c8{n7 n1} - b6n1{r4c8 .} ==> r3c7≠2 biv-chain[3]: c2n8{r2 r3} - r3n2{c2 c4} - r2c4{n2 n7} ==> r2c2≠7 naked-quads-in-a-row: r3{c1 c3 c8 c7}{n5 n7 n9 n4} ==> r3c6≠9, r3c6≠7, r3c5≠9, r3c5≠7, r3c4≠7, r3c2≠9, r3c2≠7, r3c2≠5 whip[1]: b2n7{r2c6 .} ==> r2c1≠7, r2c3≠7 whip[1]: b2n9{r2c6 .} ==> r2c2≠9, r2c3≠9 singles ==> r2c3=6, r6c1=6, r8c2=6, r8c6=4 whip[1]: c2n9{r6 .} ==> r6c3≠9 whip[5]: b4n9{r5c2 r6c2} - b4n5{r6c2 r5c1} - r5c7{n5 n7} - b3n7{r1c7 r3c8} - r3c1{n7 .} ==> r5c2≠3 whip[8]: b4n9{r5c2 r6c2} - b4n5{r6c2 r5c1} - b1n5{r2c1 r2c2} - r2c9{n5 n2} - r1c7{n2 n7} - r5c7{n7 n3} - r5c4{n3 n7} - r2c4{n7 .} ==> r5c2≠1 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠1 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠3 whip[8]: r7n9{c5 c6} - r7n8{c6 c7} - r9n8{c7 c6} - r2c6{n8 n7} - r2c4{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c8} - r7n6{c8 .} ==> r7c5≠7 g-whip[8]: r3n4{c7 c8} - r3n9{c8 c3} - b1n7{r3c3 r1c123} - r1c7{n7 n2} - r6n2{c7 c9} - c9n7{r6 r789} - r9c8{n7 n1} - b6n1{r4c8 .} ==> r3c7≠7 g-whip[9]: r7n6{c8 c7} - b9n5{r7c7 r789c9} - r2c9{n5 n2} - r1c7{n2 n7} - r4c7{n7 n3} - r5c7{n3 n5} - r6n5{c9 c2} - r2n5{c2 c1} - c1n4{r2 .} ==> r7c8≠4

leading to an anti-tridagon with only 5 guardians:

Code: Select all: +----------------------+----------------------+----------------------+ ! 137 1237 1379 ! 4 5 6 ! 27 8 29 ! ! 45 2458 6 ! 27 789 789 ! 1 3 25 ! ! 57 28 79 ! 123 138 138 ! 45 4579 6 ! +----------------------+----------------------+----------------------+ ! 2 137 8 ! 9 137 5 ! 367 167 4 ! ! 1357 579 4 ! 137 6 2 ! 357 1579 8 ! ! 6 13579 137 ! 8 4 137 ! 2357 1579 123579 ! +----------------------+----------------------+----------------------+ ! 1347 1347 2 ! 1357 89 13789 ! 34568 1567 1357 ! ! 8 6 137 ! 135 137 4 ! 9 2 1357 ! ! 9 1347 5 ! 6 2 1378 ! 348 147 137 ! +----------------------+----------------------+----------------------+ OR5-anti-tridagon[12] for digits 1, 3 and 7 in blocks: b4, with cells: r4c2, r5c1, r6c3 b5, with cells: r4c5, r5c4, r6c6 b7, with cells: r9c2, r7c1, r8c3 b8, with cells: r9c6, r7c4, r8c5 with 5 guardians: n5r5c1 n4r7c1 n5r7c4 n4r9c2 n8r9c6

Here is now the interesting part:
Trid-OR5-whip[7]: r7n6{c8 c7} - c7n8{r7 r9} - c7n4{r9 r3} - r3n5{c7 c1} - r2c1{n5 n4} - OR5{{n4r7c1 n8r9c6 n5r7c4 n5r5c1 | n4r9c2}} - c8n4{r9 .} ==> r7c8≠5
z-chain[3]: c8n5{r6 r3} - r2c9{n5 n2} - r6n2{c9 .} ==> r6c7≠5
t-whip[4]: r1c7{n7 n2} - r2c9{n2 n5} - b9n5{r8c9 r7c7} - c7n6{r7 .} ==> r4c7≠7
Trid-OR5-whip[6]: r2n5{c2 c9} - b9n5{r8c9 r7c7} - c7n8{r7 r9} - b9n4{r9c7 r9c8} - OR5{{n4r9c2 n8r9c6 n5r7c4 n5r5c1 | n4r7c1}} - r2c1{n4 .} ==> r3c1≠5

The end is trivial for a puzzle in T&E(3):

Code: Select all: singles ==> r3c1=7, r3c3=9,> r1c9=9, r1c7=7, r2c9=2, r2c4=7, r3c4=2, r3c2=8, r1c2=2, r6c7=2 hidden-pairs-in-a-row: r5{n7 n9}{c2 c8} ==> r5c8≠5, r5c8≠1, r5c2≠5 finned-x-wing-in-columns: n7{c5 c3}{r8 r4} ==> r4c2≠7 finned-x-wing-in-columns: n7{c3 c5}{r8 r6} ==> r6c6≠7 hidden-single-in-a-block ==> r4c5=7 naked-pairs-in-a-column: c6{r3 r6}{n1 n3} ==> r9c6≠3, r9c6≠1, r7c6≠3, r7c6≠1 finned-x-wing-in-rows: n1{r4 r9}{c2 c8} ==> r7c8≠1 finned-x-wing-in-rows: n3{r4 r9}{c2 c7} ==> r7c7≠3 biv-chain[3]: b4n5{r6c2 r5c1} - r5c7{n5 n3} - b5n3{r5c4 r6c6} ==> r6c2≠3 biv-chain[3]: r4c2{n3 n1} - r5n1{c1 c4} - b5n3{r5c4 r6c6} ==> r6c3≠3 biv-chain[3]: r6c3{n1 n7} - r5n7{c2 c8} - c8n9{r5 r6} ==> r6c8≠1 z-chain[3]: c8n6{r7 r4} - b6n1{r4c8 r6c9} - c9n7{r6 .} ==> r7c8≠7 singles ==> r7c8=6, r4c8=1, r4c2=3, r4c7=6 whip[1]: r9n3{c9 .} ==> r7c9≠3, r8c9≠3 finned-swordfish-in-columns: n1{c6 c5 c2}{r6 r3 r8} ==> r8c3≠1 biv-chain[3]: r6c6{n1 n3} - c9n3{r6 r9} - r9n1{c9 c2} ==> r6c2≠1 whip[1]: c2n1{r9 .} ==> r7c1≠1 biv-chain[3]: c1n3{r7 r1} - c1n1{r1 r5} - r5c4{n1 n3} ==> r7c4≠3 stte

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#5340 T&E(3) min-expand

#5340 T&E(3) min-expand

Re: #5340 T&E(3) min-expand

Re: #5340 T&E(3) min-expand

Re: #5340 T&E(3) min-expand

Re: #5340 T&E(3) min-expand

Re: #5340 T&E(3) min-expand