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Website · by **denis_berthier** » Fri Sep 23, 2022 4:20 pm

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Code: Select all: +-------+-------+-------+ ! 1 2 . ! . . . ! 7 8 . ! ! . . 7 ! . 8 . ! 2 . 6 ! ! . 6 8 ! . 2 . ! . 1 4 ! +-------+-------+-------+ ! 2 . . ! . . . ! 8 4 . ! ! . 4 . ! . . . ! . . . ! ! 7 8 . ! . . 4 ! 6 . 1 ! +-------+-------+-------+ ! . . . ! . 7 . ! 1 6 . ! ! 6 7 . ! 5 . . ! . . . ! ! . 1 . ! 9 6 3 ! . . . ! +-------+-------+-------+ 12....78...7.8.2.6.68.2..142.....84..4.......78...46.1....7.16.67.5......1.963...;326;13219 SER = 11.6

Code: Select all: Resolution state after Singles and whips[1]: +-------------------------+-------------------------+-------------------------+ ! 1 2 3459 ! 346 3459 569 ! 7 8 359 ! ! 3459 359 7 ! 134 8 159 ! 2 359 6 ! ! 359 6 8 ! 37 2 579 ! 359 1 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 359 13569 ! 1367 1359 15679 ! 8 4 3579 ! ! 359 4 13569 ! 123678 1359 1256789 ! 359 23579 23579 ! ! 7 8 359 ! 23 359 4 ! 6 2359 1 ! +-------------------------+-------------------------+-------------------------+ ! 34589 359 23459 ! 248 7 28 ! 1 6 23589 ! ! 6 7 2349 ! 5 14 128 ! 349 239 2389 ! ! 458 1 245 ! 9 6 3 ! 45 257 2578 ! +-------------------------+-------------------------+-------------------------+ 176 candidates.

by **DEFISE** » Sat Sep 24, 2022 8:17 am

Hidden pairs: 16c3r45 => -3r4c3 -5r4c3 -9r4c3 -3r5c3 -5r5c3 -9r5c3

Tridagon (3,5,9) in b1p357, b3p357, b4p249, b6p348
as previous puzzle but with 3 guardians: 4r1c3, 7r4c9, 2r6c8

whip[3]: r2n1{c4 c6}- r8n1{c6 c5}- c5n4{r8 .} => -4r2c4
Single: 4r2c1 (=> guardian 4r1c3 deleted)

Code: Select all: |-----------------------------------------------------------------------------| | 1 2 359 | 346 3459 569 | 7 8 359 | | 4 359 7 | 13 8 159 | 2 359 6 | | 359 6 8 | 37 2 579 | 359 1 4 | |-----------------------------------------------------------------------------| | 2 359 16 | 1367 1359 15679 | 8 4 3579 | | 359 4 16 | 123678 1359 1256789 | 359 23579 23579 | | 7 8 359 | 23 359 4 | 6 2359 1 | |-----------------------------------------------------------------------------| | 3589 359 23459 | 248 7 28 | 1 6 23589 | | 6 7 2349 | 5 14 128 | 349 239 2389 | | 58 1 245 | 9 6 3 | 45 257 2578 | |-----------------------------------------------------------------------------|

whip[7]: r6c4{n2 n3}- c5n3{r6 r1}- c5n4{r1 r8}- r7n4{c4 c3}- c3n3{r7 r8}- r8c7{n3 n9}- r8c8{n9 .} => -2r6c8
Single : 2r6c4
Only one guardian remaining: +7r4c9
Single(s): 7r9c8
Hidden pairs: 78r5c46 => -1r5c4 -3r5c4 -6r5c4 -1r5c6 -5r5c6 -6r5c6 -9r5c6
Single(s): 6r5c3, 1r4c3, 1r5c5, 4r8c5, 8r7c4, 7r5c4, 3r3c4, 1r2c4, 6r4c4, 4r1c4, 8r5c6, 2r7c6, 1r8c6, 6r1c6, 7r3c6, 4r7c3, 8r8c9, 4r9c7, 8r9c1
Box/Line: 5b9c9 => -5r1c9 -5r5c9
whip[3]: r2n3{c8 c2}- c3n3{r1 r8}- c7n3{r8 .} => -3r6c8
Box/Line: 3b6r5 => -3r5c1
Single(s): 3r7c1
Xwing in columns: 5c17r35 => -5r5c8
whip[4]: r2n3{c8 c2}- c3n3{r1 r6}- r6n5{c3 c5}- c6n5{r4 .} => -5r2c8
Single(s): 5r6c8, 5r5c1, 9r3c1, 5r3c7
whip[3]: r6n9{c3 c5}- r1n9{c5 c9}- r7n9{c9 .} => -9r8c3
STTE

by **Cenoman** » Sat Sep 24, 2022 8:47 pm

Three steps (no preliminary elimination of a TH guardian)

Code: Select all: +------------------------+----------------------------+------------------------+ | 1 2 a3459* | 346 b3459 569 | 7 8 359** | | 3459 359* 7 | 134 8 159 | 2 359* 6 | | 359* 6 8 | 37 2 579 | 359* 1 4 | +------------------------+----------------------------+------------------------+ | 2 359* 13569 | 1367 z1359 15679 | 8 4 A3579* | | B359* 4 13569 | 123678 zB1359 1256789 | B359* B23579 B23579 | | 7 8 359* | y23 z359 4 | 6 x2359* 1 | +------------------------+----------------------------+------------------------+ | 34589 359 23459 | 248 7 28 | 1 6 23589 | | 6 7 2349 | 5 c4-1 128 | 349 239 2389 | | 458 1 245 | 9 6 3 | 45 257 2578 | +------------------------+----------------------------+------------------------+

1. TH(359)b1346 having three guardians: 4r1c3, 7r4c9, 2r6c8
(4)r1c3 - r1c5 = (4)r8c5
(7)r4c9 - (7=23591)r5c15789
(2)r6c8 - (2=3)r6c4 - (3=591)r456c5
=> -1 r8c5; 9 placements

Code: Select all: +--------------------+-----------------------+------------------------+ | 1 2 b359 | 4 b359 6 | 7 8 359 | | 4 359 7 | 1 8 59 | 2 359 6 | | 359 6 8 | b37 2 579 | 359 1 4 | +--------------------+-----------------------+------------------------+ | 2 359 16 | 367 1359 579 | 8 4 359+7 | | 359 4 16 | 23678 1359 28 | 359 23579 23579 | | 7 8 b359 | a23 359 4 | 6 359-2 1 | +--------------------+-----------------------+------------------------+ | 359 359 4 | 28 7 28 | 1 6 2359 | | 6 7 c239 | 5 4 1 | 39 d239 8 | | 8 1 25 | 9 6 3 | 4 257 257 | +--------------------+-----------------------+------------------------+

2. (2=3)r6c4 - [r3c4 = r1c5 - r1c3 = r6c3] = (3-2)r8c3 = (2)r8c8 => -2 r6c8; 4 placements
TH(359)b1346 has now a single guardian => +7 r4c9; 8 further placements

Code: Select all: +--------------------+------------------+----------------------+ | 1 2 f359^ | 4 59* 6 | 7 8 f359^ | | 4 359 7 | 1 8 59* | 2 a#359* 6 | | 59 6 8 | 3 2 7 | 59 1 4 | +--------------------+------------------+----------------------+ | 2 a359 1 | 6 a359 59 | 8 4 7 | | d359 4 6 | 7 1 8 | c359 c2359 c2359 | | 7 8 359 | 2 a#359* 4 | 6 b359* 1 | +--------------------+------------------+----------------------+ | e359 f359^ 4 | 8 7 2 | 1 6 f359^ | | 6 7 239 | 5 4 1 | 39 239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | +--------------------+------------------+----------------------+

3. Bivalue oddagon (*) (59)r26, c58, b2 having three guardians (#): 3r2c8, 3r6c5, 3r6c8
(3): [r4c2 = r4c5 - r6c5 == r2c8] == r6c8 - r5c789 = r5c1 - r7c1 = Skyscraper^[r7c2 = r7c9 - r1c9 = r1c3] => -3 r2c2; ste

Or presented as a kraken:

Hidden Text: Show

by **eleven** » Sun Sep 25, 2022 11:51 am

Code: Select all: +----------------------------+----------------------------+----------------------------+ | 1 2 3459 | 346 e3459 569 | 7 8 359 | | 3459 359 7 |a13-4 8 b159 | 2 359 6 | | 359 6 8 | 37 2 579 | 359 1 4 | +----------------------------+----------------------------+----------------------------+ | 2 359 16 | 1367 1359 15679 | 8 4 3579 | | 359 4 16 | 123678 1359 1256789 | 359 23579 23579 | | 7 8 359 | 23 359 4 | 6 2359 1 | +----------------------------+----------------------------+----------------------------+ | 34589 359 23459 | 248 7 28 | 1 6 23589 | | 6 7 2349 | 5 d14 c128 | 349 239 2389 | | 458 1 245 | 9 6 3 | 45 257 2578 | +----------------------------+----------------------------+----------------------------+

1r2c4 = r2c6 - r8c6 = (1-4)r8c5 = 4r1c5 => -4r2c4

Code: Select all: +----------------------------+----------------------------+----------------------------+ | 1 2 359 |c346 b3459 569 | 7 8 359 | | 4 359 7 |c13 8 159 | 2 359 6 | | 359 6 8 |c37 2 579 | 359 1 4 | +----------------------------+----------------------------+----------------------------+ | 2 359 16 | 1367 1359 15679 | 8 4 3579 | | 359 4 16 |#123678 1359 #1256789 | 359 23579 23579 | | 7 8 359 |*2-3 359 4 | 6 2359 1 | +----------------------------+----------------------------+----------------------------+ | 3589 359 23459 |#248 7 #28 | 1 6 23589 | | 6 7 2349 | 5 a14 *128 | 349 239 2389 | | 58 1 245 | 9 6 3 | 45 257 2578 | +----------------------------+----------------------------+----------------------------+

UR 28r57c46: 2r6c4 == (28-1)r8c6 = (1-4)r8c5 = (4-3)r1c5 = 3r123c4 => -3r6c4
TH: 2r6c4 => 7r4c9

Code: Select all: *-----------------------------------------------------------* | 1 2 359 | 4 59 6 | 7 8 39 | | 4 359 7 | 1 8 59 | 2 359 6 | | 59 6 8 | 3 2 7 | 59 1 4 | |--------------------+----------------+---------------------| | 2 359 1 | 6 359 59 | 8 4 7 | | *359 4 6 | 7 1 8 | *359 2359 239 | | 7 8 359 | 2 359 4 | 6 359 1 | |--------------------+----------------+---------------------| | *359 359 4 | 8 7 2 | 1 6 59-3 | | 6 7 29-3 | 5 4 1 | *39 239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | *-----------------------------------------------------------*

skysraper 3c17 => -3r8c3,r7c9

Code: Select all: *----------------------------------------------------------* | 1 2 #359 | 4 #59 6 | 7 8 39 | | 4 59-3 7 | 1 8 #59 | 2 359 6 | | #59 6 8 | 3 2 7 | 59 1 4 | |-------------------+----------------+---------------------| | 2 #359 1 | 6 359 #59 | 8 4 7 | | #59 4 6 | 7 1 8 | 359 2359 239 | | 7 8 59-3 | 2 359 4 | 6 59 1 | |-------------------+----------------+---------------------| | 3 59 4 | 8 7 2 | 1 6 59 | | 6 7 29 | 5 4 1 | 39 239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | *----------------------------------------------------------*

Oddagon 59: 3r1c3 = 3r4c2 => -3r6c3, ste

Website · by **denis_berthier** » Sun Sep 25, 2022 3:49 pm

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Thanks for your solutions;
As you have noticed, this puzzle is a variant of #1888. It also allows lots of direct tridagon eliminations.
Solved with chains of lengths ≤ 4.

It illustrates that puzzles in the min-expand database can be similar, though not equivalent.

Code: Select all: hidden-pairs-in-a-column: c3{n1 n6}{r4 r5} ==> r5c3≠9, r5c3≠5, r5c3≠3, r4c3≠9, r4c3≠5, r4c3≠3 finned-x-wing-in-rows: n4{r2 r7}{c4 c1} ==> r9c1≠4 biv-chain[3]: r2n1{c4 c6} - b8n1{r8c6 r8c5} - b8n4{r8c5 r7c4} ==> r2c4≠4 hidden-single-in-a-row ==> r2c1=4 z-chain[3]: c4n8{r5 r7} - b8n4{r7c4 r8c5} - c5n1{r8 .} ==> r5c4≠1 +-------------------------+-------------------------+-------------------------+ ! 1 2 359 ! 346 3459 569 ! 7 8 359 ! ! 4 359 7 ! 13 8 159 ! 2 359 6 ! ! 359 6 8 ! 37 2 579 ! 359 1 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 359 16 ! 1367 1359 15679 ! 8 4 3579 ! ! 359 4 16 ! 23678 1359 1256789 ! 359 23579 23579 ! ! 7 8 359 ! 23 359 4 ! 6 2359 1 ! +-------------------------+-------------------------+-------------------------+ ! 3589 359 23459 ! 248 7 28 ! 1 6 23589 ! ! 6 7 2349 ! 5 14 128 ! 349 239 2389 ! ! 58 1 245 ! 9 6 3 ! 45 257 2578 ! +-------------------------+-------------------------+-------------------------+ OR2-anti-tridagon[12] for digits 3, 5 and 9 in blocks: b1, with cells: r1c3, r2c2, r3c1 b3, with cells: r1c9, r2c8, r3c7 b4, with cells: r6c3, r4c2, r5c1 b6, with cells: r6c8, r4c9, r5c7 with 2 guardians: n7r4c9 n2r6c8 Trid-OR2-forcing-whip-elim[2]: || n2r6c8 - || n7r4c9 - partial-whip[1]: c8n7{r5 r9} - ==> r9c8≠2 Trid-OR2-forcing-whip-elim[3]: || n7r4c9 - || n2r6c8 - partial-whip[2]: r6c4{n2 n3} - r3c4{n3 n7} - ==> r4c4≠7 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠9 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠6 t-whip[4]: r5n1{c6 c3} - r5n6{c3 c4} - r5n8{c4 c6} - b5n7{r5c6 .} ==> r4c6≠1 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠5 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠1 biv-chain[4]: r5n8{c6 c4} - r5n6{c4 c3} - r5n1{c3 c5} - b8n1{r8c5 r8c6} ==> r8c6≠8 singles ==> r8c9=8, r9c1=8 biv-chain[4]: c4n8{r7 r5} - r5n6{c4 c3} - r5n1{c3 c5} - r8c5{n1 n4} ==> r7c4≠4 singles ==> r8c5=4, r1c4=4, r1c6=6, r8c6=1, r2c4=1, r9c7=4, r7c3=4 whip[1]: b8n2{r7c6 .} ==> r7c9≠2 hidden-pairs-in-a-column: c6{n2 n8}{r5 r7} ==> r5c6≠7 Trid-OR2-forcing-whip-elim[2]: || n7r4c9 - || n2r6c8 - partial-whip[1]: b9n2{r8c8 r9c9} - ==> r9c9≠7 hidden-single-in-a-block ==> r9c8=7 whip[1]: b9n5{r9c9 .} ==> r1c9≠5, r4c9≠5, r5c9≠5 biv-chain[3]: r4c4{n3 n6} - r5n6{c4 c3} - r5n1{c3 c5} ==> r5c5≠3 Trid-OR2-forcing-whip-elim[3]: || n2r6c8 - partial-whip[1]: r6c4{n2 n3} - || n7r4c9 - partial-whip[1]: r5n7{c9 c4} - ==> r5c4≠3 biv-chain[4]: r4n7{c9 c6} - r3n7{c6 c4} - b2n3{r3c4 r1c5} - r1c9{n3 n9} ==> r4c9≠9 biv-chain[3]: r4c4{n6 n3} - r4c9{n3 n7} - b5n7{r4c6 r5c4} ==> r5c4≠6 singles ==> r4c4=6, r4c3=1, r5c3=6, r5c5=1 z-chain[4]: c4n3{r6 r3} - c7n3{r3 r8} - c3n3{r8 r1} - r2n3{c2 .} ==> r6c8≠3 z-chain[4]: c5n3{r6 r1} - c3n3{r1 r8} - r8n2{c3 c8} - r6n2{c8 .} ==> r6c4≠3 singles ==> r6c4=2, r5c6=8, r5c4=7, r3c4=3, r7c6=2, r7c4=8, r3c6=7, r4c9=7 whip[1]: b6n3{r5c9 .} ==> r5c1≠3 hidden-single-in-a-column ==> r7c1=3 x-wing-in-columns: n5{c1 c7}{r3 r5} ==> r5c8≠5 finned-x-wing-in-columns: n5{c8 c6}{r2 r6} ==> r6c5≠5 whip[1]: b5n5{r4c6 .} ==> r4c2≠5 biv-chain[3]: r7n9{c2 c9} - r1c9{n9 n3} - b1n3{r1c3 r2c2} ==> r2c2≠9 biv-chain[3]: r2n9{c6 c8} - r2n3{c8 c2} - r4c2{n3 n9} ==> r4c6≠9 singles ==> r4c6=5, r2c6=9, r1c5=5 finned-x-wing-in-rows: n9{r1 r8}{c3 c9} ==> r7c9≠9 stte

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