The New Sudoku Players' Forum

by **coloin** » Fri Sep 06, 2024 3:06 pm

Code: Select all: +---+---+---+ |...|.58|4..| |...|4.6|7..| |...|79.|8..| +---+---+---+ |.86|..4|...| |4.7|9..|...| |59.|.6.|...| +---+---+---+ |65.|...|9..| |...|..9|5.1| |..9|...|.2.| +---+---+---+ DoubleTrouble

This has high -q2 and suexratt but 11.7 only ... maybe DoubleTrouble for y'all !

by **P.O.** » Fri Sep 06, 2024 4:55 pm

this is the second puzzle i see that requires 3 runs of the combinations of 6 templates to solve:
(2 4 5 6 4 4 5 6 3 3 4 4 5 3 4 5 4 5 4 6 2 3 2 2 3 3 2 2 2) puzzle in 6(3)-Template
the other one is Shining Mirror by Mauricio:
(2 4 5 5 6 6 5 5 5 6 2) puzzle in 6(3)-Template

Website · by **denis_berthier** » Sat Sep 07, 2024 3:23 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 12379 12367 123 ! 123 5 8 ! 4 1369 2369 ! ! 12389 123 12358 ! 4 123 6 ! 7 1359 2359 ! ! 123 12346 12345 ! 7 9 123 ! 8 1356 2356 ! +----------------------+----------------------+----------------------+ ! 123 8 6 ! 1235 1237 4 ! 123 3579 3579 ! ! 4 123 7 ! 9 1238 1235 ! 1236 3568 3568 ! ! 5 9 123 ! 1238 6 1237 ! 123 3478 3478 ! +----------------------+----------------------+----------------------+ ! 6 5 12348 ! 1238 123478 1237 ! 9 3478 3478 ! ! 2378 2347 2348 ! 2368 23478 9 ! 5 34678 1 ! ! 1378 1347 9 ! 13568 13478 1357 ! 36 2 34678 ! +----------------------+----------------------+----------------------+ 221 candidates.

naked-triplets-in-a-block: b1{r1c3 r2c2 r3c1}{n3 n2 n1} ==> r3c3≠3, r3c3≠2, r3c3≠1, r3c2≠3, r3c2≠2, r3c2≠1, r2c3≠3, r2c3≠2, r2c3≠1, r2c1≠3, r2c1≠2, r2c1≠1, r1c2≠3, r1c2≠2, r1c2≠1, r1c1≠3, r1c1≠2, r1c1≠1

As in the previous puzzle (MagicJim), there are two tridagons (with the same digits, and necessarily in the same blocks).
Both of them are used in the resolution path:

Code: Select all: Trid-OR3-relation for digits 1, 2 and 3 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c4, r5c6, r4c5 with 3 guardians (in cells marked @): n7r4c5 n5r5c6 n8r6c4 +----------------------+----------------------+----------------------+ ! 79 67 123# ! 123# 5 8 ! 4 1369 2369 ! ! 89 123# 58 ! 4 123# 6 ! 7 1359 2359 ! ! 123# 46 45 ! 7 9 123# ! 8 1356 2356 ! +----------------------+----------------------+----------------------+ ! 123# 8 6 ! 1235 1237#@ 4 ! 123 3579 3579 ! ! 4 123# 7 ! 9 1238 1235#@ ! 1236 3568 3568 ! ! 5 9 123# ! 1238#@ 6 1237 ! 123 3478 3478 ! +----------------------+----------------------+----------------------+ ! 6 5 12348 ! 1238 123478 1237 ! 9 3478 3478 ! ! 2378 2347 2348 ! 2368 23478 9 ! 5 34678 1 ! ! 1378 1347 9 ! 13568 13478 1357 ! 36 2 34678 ! +----------------------+----------------------+----------------------+ Trid-OR3-relation for digits 1, 2 and 3 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c6, r5c5, r4c4 with 3 guardians (in cells marked @): n5r4c4 n8r5c5 n7r6c6 +----------------------+----------------------+----------------------+ ! 79 67 123# ! 123# 5 8 ! 4 1369 2369 ! ! 89 123# 58 ! 4 123# 6 ! 7 1359 2359 ! ! 123# 46 45 ! 7 9 123# ! 8 1356 2356 ! +----------------------+----------------------+----------------------+ ! 123# 8 6 ! 1235#@ 1237 4 ! 123 3579 3579 ! ! 4 123# 7 ! 9 1238#@ 1235 ! 1236 3568 3568 ! ! 5 9 123# ! 1238 6 1237#@ ! 123 3478 3478 ! +----------------------+----------------------+----------------------+ ! 6 5 12348 ! 1238 123478 1237 ! 9 3478 3478 ! ! 2378 2347 2348 ! 2368 23478 9 ! 5 34678 1 ! ! 1378 1347 9 ! 13568 13478 1357 ! 36 2 34678 ! +----------------------+----------------------+----------------------+

Trid-OR3-whip[8]: r8n6{c4 c8} - r9n6{c9 c4} - r9n5{c4 c6} - OR3{{n5r5c6 n8r6c4 | n7r4c5}} - b8n7{r7c5 r7c6} - c8n7{r7 r6} - r6n4{c8 c9} - r6n8{c9 .} ==> r8c4≠8

Here again, eleven's replacement technique is key to the solution :

Code: Select all: +----------------------+----------------------+----------------------+ ! 79 67 123 ! 123 5 8 ! 4 1369 2369 ! ! 89 123 58 ! 4 123 6 ! 7 1359 2359 ! ! 123 46 45 ! 7 9 123 ! 8 1356 2356 ! +----------------------+----------------------+----------------------+ ! 123 8 6 ! 1235 1237 4 ! 123 3579 3579 ! ! 4 123 7 ! 9 1238 1235 ! 1236 3568 3568 ! ! 5 9 123 ! 1238 6 1237 ! 123 3478 3478 ! +----------------------+----------------------+----------------------+ ! 6 5 12348 ! 1238 123478 1237 ! 9 3478 3478 ! ! 2378 2347 2348 ! 236 23478 9 ! 5 34678 1 ! ! 1378 1347 9 ! 13568 13478 1357 ! 36 2 34678 ! +----------------------+----------------------+----------------------+ ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE ***** RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens. Trying in block 4 +-------------------------+-------------------------+-------------------------+ ! 79 67 123 ! 123 5 8 ! 4 12369 12369 ! ! 89 123 58 ! 4 123 6 ! 7 12359 12359 ! ! 123 46 45 ! 7 9 123 ! 8 12356 12356 ! +-------------------------+-------------------------+-------------------------+ ! 3 8 6 ! 1235 1237 4 ! 123 123579 123579 ! ! 4 2 7 ! 9 1238 1235 ! 1236 123568 123568 ! ! 5 9 1 ! 1238 6 1237 ! 123 123478 123478 ! +-------------------------+-------------------------+-------------------------+ ! 6 5 12348 ! 1238 123478 1237 ! 9 123478 123478 ! ! 12378 12347 12348 ! 1236 123478 9 ! 5 1234678 123 ! ! 12378 12347 9 ! 123568 123478 12357 ! 1236 123 1234678 ! +-------------------------+-------------------------+-------------------------+

Trid-OR3-whip[5]: r6c7{n2 n3} - r6c6{n3 n7} - OR3{{n7r4c5 n8r6c4 | n5r5c6}} - r5n3{c6 c5} - b5n8{r5c5 .} ==> r6c4≠2
z-chain[3]: r4c7{n1 n2} - b5n2{r4c4 r6c6} - b5n7{r6c6 .} ==> r4c5≠1
Trid-OR3-whip[4]: r6c4{n3 n8} - OR3{{n8r5c5 n7r6c6 | n5r4c4}} - b5n2{r4c4 r4c5} - b5n7{r4c5 .} ==> r6c6≠3
naked-pairs-in-a-block: b5{r4c5 r6c6}{n2 n7} ==> r4c4≠2
biv-chain[4]: r9n5{c6 c4} - r4c4{n5 n1} - r4c7{n1 n2} - b5n2{r4c5 r6c6} ==> r9c6≠2
Trid-OR3-whip[5]: r4c7{n1 n2} - r6n2{c9 c6} - OR3{{n7r6c6 n5r4c4 | n8r5c5}} - r6c4{n8 n3} - r6c7{n3 .} ==> r4c4≠1
singles ==> r4c4=5, r9c6=5

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 79 67 23 ! 123 5 8 ! 4 12369 12369 ! ! 89 13 58 ! 4 123 6 ! 7 12359 12359 ! ! 12 46 45 ! 7 9 123 ! 8 12356 12356 ! +-------------------------+-------------------------+-------------------------+ ! 3 8 6 ! 5 27 4 ! 12 1279 1279 ! ! 4 2 7 ! 9 138 13 ! 136 13568 13568 ! ! 5 9 1 ! 38 6 27 ! 23 23478 23478 ! +-------------------------+-------------------------+-------------------------+ ! 6 5 2348 ! 1238 123478 1237 ! 9 123478 123478 ! ! 1278 1347 2348 ! 1236 123478 9 ! 5 1234678 123 ! ! 1278 1347 9 ! 12368 123478 5 ! 1236 123 1234678 ! +-------------------------+-------------------------+-------------------------+ At least one candidate of a previous Trid-OR3-relation between candidates n7r4c5 n5r5c6 n8r6c4 has just been eliminated. There remains a Trid-OR2-relation between candidates: n7r4c5 n8r6c4

whip[1]: r4n1{c9 .} ==> r5c7≠1, r5c8≠1, r5c9≠1
Trid-OR2-whip[3]: OR2{{n8r6c4 | n7r4c5}} - b5n2{r4c5 r6c6} - r6c7{n2 .} ==> r6c4≠3

The end is in W9, with nothing noticeable:

Code: Select all: naked-single ==> r6c4=8 whip[1]: r6n3{c9 .} ==> r5c9≠3, r5c8≠3, r5c7≠3 naked-single ==> r5c7=6 naked-triplets-in-a-block: b9{r8c9 r9c7 r9c8}{n2 n1 n3} ==> r9c9≠3, r9c9≠2, r9c9≠1, r8c8≠3, r8c8≠2, r8c8≠1, r7c9≠3, r7c9≠2, r7c9≠1, r7c8≠3, r7c8≠2, r7c8≠1 whip[1]: r7n1{c4 .} ==> r8c4≠1, r8c5≠1, r9c4≠1, r9c5≠1 whip[5]: c4n3{r9 r1} - r1c3{n3 n2} - r3c1{n2 n1} - b2n1{r3c6 r2c5} - r5c5{n1 .} ==> r8c5≠3 whip[5]: c4n3{r9 r1} - r1c3{n3 n2} - r3c1{n2 n1} - b2n1{r3c6 r2c5} - r5c5{n1 .} ==> r7c5≠3 whip[4]: c4n2{r9 r1} - r1c3{n2 n3} - r7n3{c3 c4} - c4n1{r7 .} ==> r7c6≠2 whip[5]: c4n3{r9 r1} - c4n1{r1 r7} - r7n3{c4 c3} - r7n2{c3 c5} - c4n2{r7 .} ==> r9c5≠3 whip[5]: r5c6{n1 n3} - r3c6{n3 n2} - b1n2{r3c1 r1c3} - b1n3{r1c3 r2c2} - c5n3{r2 .} ==> r7c6≠1 z-chain[5]: c5n3{r5 r2} - b1n3{r2c2 r1c3} - r7n3{c3 c4} - r7n1{c4 c5} - r5c5{n1 .} ==> r5c6≠3 singles ==> r5c6=1, r5c5=3 biv-chain[3]: r2c5{n2 n1} - r2c2{n1 n3} - r1c3{n3 n2} ==> r1c4≠2 whip[1]: c4n2{r9 .} ==> r8c5≠2, r7c5≠2, r9c5≠2 biv-chain[3]: r1c3{n3 n2} - r7n2{c3 c4} - c4n1{r7 r1} ==> r1c4≠3 singles ==> r1c4=1, r2c5=2, r3c6=3, r7c6=7, r6c6=2, r6c7=3, r4c5=7, r7c5=1 naked-pairs-in-a-block: b9{r7c8 r7c9}{n4 n8} ==> r9c9≠8, r9c9≠4, r8c8≠8, r8c8≠4 whip[1]: b9n4{r7c8 .} ==> r7c3≠4 whip[1]: b9n8{r7c8 .} ==> r7c3≠8 naked-pairs-in-a-column: c3{r1 r7}{n2 n3} ==> r8c3≠3, r8c3≠2 naked-pairs-in-a-row: r8{c3 c5}{n4 n8} ==> r8c2≠4, r8c1≠8 whip[9]: r9c7{n2 n1} - r9c8{n1 n3} - r9c4{n3 n6} - r9c9{n6 n7} - r9c2{n7 n4} - r3c2{n4 n6} - c9n6{r3 r1} - r1n3{c9 c3} - c3n2{r1 .} ==> r9c1≠2 whip[9]: c1n2{r8 r3} - b3n2{r3c8 r1c8} - r9n2{c8 c4} - r9n6{c4 c9} - b3n6{r3c9 r3c8} - r3n1{c8 c9} - r4c9{n1 n9} - r1c9{n9 n3} - r1c3{n3 .} ==> r8c9≠2 whip[1]: b9n2{r9c8 .} ==> r9c4≠2 whip[5]: r8n6{c8 c4} - r9c4{n6 n3} - r7n3{c4 c3} - r1n3{c3 c9} - r8n3{c9 .} ==> r1c8≠6 biv-chain[3]: b1n7{r1c1 r1c2} - r1n6{c2 c9} - r9c9{n6 n7} ==> r9c1≠7 whip[5]: r2n5{c8 c3} - c3n8{r2 r8} - r9c1{n8 n1} - b9n1{r9c7 r8c9} - r3n1{c9 .} ==> r3c8≠5 whip[4]: r3c1{n1 n2} - r8n2{c1 c4} - r8n6{c4 c8} - r3c8{n6 .} ==> r3c9≠1 whip[5]: r2c2{n3 n1} - r3n1{c1 c8} - r9c8{n1 n2} - r4c8{n2 n9} - r1c8{n9 .} ==> r2c8≠3 finned-x-wing-in-columns: n3{c8 c3}{r1 r9} ==> r9c2≠3 biv-chain[3]: b1n1{r3c1 r2c2} - r2n3{c2 c9} - r8c9{n3 n1} ==> r8c1≠1 biv-chain[4]: r2n3{c9 c2} - b1n1{r2c2 r3c1} - r9c1{n1 n8} - r2c1{n8 n9} ==> r2c9≠9 biv-chain[4]: r1n6{c9 c2} - r1n7{c2 c1} - r8c1{n7 n2} - b1n2{r3c1 r1c3} ==> r1c9≠2 biv-chain[4]: c1n7{r1 r8} - c1n2{r8 r3} - c9n2{r3 r4} - c9n9{r4 r1} ==> r1c1≠9 singles ==> r1c1=7, r1c2=6, r3c2=4, r3c3=5, r2c3=8, r2c1=9, r8c3=4, r8c5=8, r9c5=4, r8c1=2, r3c1=1, r2c2=3, r1c3=2, r9c1=8, r7c3=3, r7c4=2 biv-chain[4]: c7n1{r4 r9} - r8c9{n1 n3} - r1n3{c9 c8} - c8n9{r1 r4} ==> r4c8≠1 biv-chain[5]: c8n6{r3 r8} - r9n6{c9 c4} - r9n3{c4 c8} - r1c8{n3 n9} - r4c8{n9 n2} ==> r3c8≠2 stte

by **yzfwsf** » Sat Sep 07, 2024 7:53 am

After the following steps:

Code: Select all: Locked Candidates 2 (Claiming): 1 in c7 => r4c8<>1,r5c8<>1,r6c8<>1 Locked Candidates 2 (Claiming): 2 in c7 => r4c9<>2,r5c9<>2,r6c9<>2 Naked Triple: in r1c3,r2c2,r3c1 => r1c1<>123,r1c2<>123,r2c1<>123,r2c3<>123,r3c2<>123,r3c3<>123, Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r4c4<>1,r4c4<>2,r4c4<>3,r4c89,r5c6,r9c4<>5 5r4c4 8r5c5 - (8=12365)b6p14567 - 5r5c6 = 5r4c4 7r6c6 - (7=1235)r4c1457 Hidden Single: 5 in r4 => r4c4=5 Hidden Single: 5 in r9 => r9c6=5 ALS Discontinuous Nice Loop with Triplet Oddagon(r16c34,r2c25,r3c16,r4c15,r5c26): (6=1238)r5c2567 - r6c4 = 7r4c5 - (7=12396)b6p12347 => r5c7=6 Naked Single: r9c7=3 Discontinuous Nice Loop with Triplet Oddagon(r16c34,r2c25,r3c16,r4c15,r5c26): (8=1237)r6c3467 - r4c5 = 8r6c4 => r6c4=8 Hidden Pair: 58 in r5c8,r5c9 => r5c8<>3,r5c9<>3 Almost Locked Triple: 478 in r7c56 r89c5 r7c89 => r7c3<>48 r8c5<>23 r9c5<>1 Naked Triple: in r1c3,r6c3,r7c3 => r8c3<>23

Code: Select all: ,-----------------,-------------------,----------------, | 79 67 123 | 123 5 8 | 4 1369 2369 | | 89 123 58 | 4 123 6 | 7 1359 2359 | | 123 46 45 | 7 9 123 | 8 1356 2356 | :-----------------+-------------------+----------------: | 123 8 6 | 5 1237 4 | 12 379 379 | | 4 123 7 | 9 123 123 | 6 58 58 | | 5 9 123 | 8 6 1237 | 12 347 347 | :-----------------+-------------------+----------------: | 6 5 123 | 123 123478 1237 | 9 478 478 | | 2378 2347 48 | 236 478 9 | 5 4678 1 | | 178 147 9 | 16 478 5 | 3 2 4678 | '-----------------'-------------------'----------------'

Assuming r4c5<>7, there are the following step：
Triplet Oddagon(RT) + Triplet ERI: 123r16c34,r2c25,r3c16,r4c15,r5c26 + 123b8 => r7c3<>123
This is obviously contradictory, so r4c5=7.
At this point, the skfr difficulty is 9.0.

by **DEFISE** » Sat Sep 07, 2024 10:12 am

Similar start to the previous puzzle, but much more difficult at the end.
That is to say that I validate in the same way a guardian of the 1st tridagon then a guardian of the 2nd tridagon.
But after that the puzzle is not even solvable in T&E(S4,1). In fact it is in B2B (at the beginning the puzzle is in B6B).
Yesterday's puzzle is in B10B but the Tridagon-rules are more efficient.

by **totuan** » Sat Sep 07, 2024 4:52 pm

Code: Select all: *-----------------------------------------------------------------------------* | 79 67 T123 |T123 5 8 | 4 1369 2369 | | 89 T123 58 | 4 T123 6 | 7 1359 2359 | |T123 46 45 | 7 9 T123 | 8 1356 2356 | |-------------------------+-------------------------+-------------------------| |T123 8 6 |B1235 A1237 4 | 123 3579 3579 | | 4 T123 7 | 9 B1238 A1235 | 1236 3568 3568 | | 5 9 T123 |A1238 6 B1237 | 123 3478 3478 | |-------------------------+-------------------------+-------------------------| | 6 5 12348 | 1238 123478 1237 | 9 3478 3478 | | 2378 2347 2348 | 2368 23478 9 | 5 34678 1 | | 1378 1347 9 | 13568 13478 1357 | 36 2 34678 | *-----------------------------------------------------------------------------*

My path for this one:
01: Tridagon(123) T-A & T-B marked cells => r6c4=8 & r4c4=8, some singles

Code: Select all: *-----------------------------------------------------------------------------* | 79 67 #123 |#123 5 8 | 4 1369 2369 | | 89 #123 58 | 4 #123 6 | 7 1359 2359 | |#123 46 45 | 7 9 #123 | 8 1356 2356 | |-------------------------+-------------------------+-------------------------| |#123 8 6 | 5 #123+7 4 | 12 379 379 | | 4 #123 7 | 9 #123 #123 | 6 58 58 | | 5 9 #123 | 8 6 123-7 | 12 347 347 | |-------------------------+-------------------------+-------------------------| | 6 5 #123+48 | 123 *123478 A123+7 | 9 *478 *478 | | 2378 2347 2348 | 236 23478 9 | 5 4678 1 | | 178 147 9 | 16 1478 5 | 3 2 4678 | *-----------------------------------------------------------------------------*

Impossible partern (123) # marked cells => (7)r4c5,r7c6=(48)r7c3. It's not hard for proving

02: (7)r4c5,r7c6==(478)r7c389-(478=123)r257c5-(123=7)r4c5 => r6c6<>7, some singles

Code: Select all: *-----------------------------------------------------------* | 79 67 %123 |*123 5 8 | 4 136-9 2369 | | 89 123 58 | 4 123 6 | 7 1359 2359 | | 123 46 45 | 7 9 #123 | 8 1356 2356 | |-------------------+-------------------+-------------------| | 12 8 6 | 5 7 4 | 12 39 39 | | 4 123 7 | 9 #123 &123 | 6 58 58 | | 5 9 *123 | 8 6 &123 | 12 47 47 | |-------------------+-------------------+-------------------| | 6 5 %123 |%123 *123 7 | 9 48 48 | | 237 237 48 |%236 48 9 | 5 67 1 | | 178 147 9 |%16 48 5 | 3 2 67 | *-----------------------------------------------------------*

Note:
a.(1|2|3)r1c4 lead to (1|2|3)r6c3&r7c5 by (1|2|3)B7&C3
b.(1|2|3)r3c6 lead to (1|2|3)r5c5 by ((1|2|3)B5
a&b =>(1|2|3)r1c3,r3c6 is eliminated (1|2|3)r5c2 =>(2|3)r2c9 lead to (2|3)r8c2 then eliminates (7)r8c2
c.(1)r9c4 is eliminated (1)r1c34 => lead to (1)r1c8 by 1’s B7, R17

03: Present as diagram: => r1c8<>9

Code: Select all: (2|3)r2c9--(7)r8c2 || || || (7)r8c1-(7=9)r1c1* || || || (7-6)r8c8=r8c4--(6=1)r9c4--r1c34=(1)r1c8* || | (5)r2c9-(4578=6)r6789c9-- || (9)r2c9*

Code: Select all: *-----------------------------------------------------------* | 79 67 123 | 123 5 8 | 4 13-6 2369 | | 89 123 58 | 4 123 6 | 7 1359 2359 | | 123 46 45 | 7 9 123 | 8 1356 2356 | |-------------------+-------------------+-------------------| | 12 8 6 | 5 7 4 | 12 39 39 | | 4 123 7 | 9 123 123 | 6 58 58 | | 5 9 123 | 8 6 123 | 12 47 47 | |-------------------+-------------------+-------------------| | 6 5 123 | 123 123 7 | 9 48 48 | | 237 237 48 | 236 48 9 | 5 67 1 | | 178 147 9 | 16 48 5 | 3 2 67 | *-----------------------------------------------------------*

04: Present as diagram: => r1c8<>6

Code: Select all: (1)r1c8 || (1)r1c4-------------(1=6)r9c1-r8c4=r8c8 || | (1)r1c3-r7c3=r7c45-

Code: Select all: *-----------------------------------------------------------* | 79 67 123 | 123 5 8 | 4 13 69 | | 89 123 58 | 4 123 6 | 7 359-1 2359 | | 123 46 45 | 7 9 123 | 8 1356 2356 | |-------------------+-------------------+-------------------| | 12 8 6 | 5 7 4 | 12 39 39 | | 4 123 7 | 9 123 123 | 6 58 58 | | 5 9 123 | 8 6 123 | 12 47 47 | |-------------------+-------------------+-------------------| | 6 5 123 | 123 123 7 | 9 48 48 | | 237 237 48 | 236 48 9 | 5 67 1 | | 178 147 9 | 16 48 5 | 3 2 67 | *-----------------------------------------------------------*

Note: as above, if r6c3<>1 => r1c4<>1 by 1’s on B7 & C3

05: Present as diagram: => r2c8<>1

Code: Select all: (1)r2c2* (1)r2c5* || || (1)r5c2---r5c56=r6c6-(1)r3c6 || | || || ------------(1)r6c3,r1c4 (5)r2c8* || || (1)r9c2---(4)r9c2=r8c3-(4=5)r3c3----(5)r2c3 | || -(16=7)r9c49-(478=5)r567c9-(5)r2c9

Code: Select all: *-----------------------------------------------------------* | 79 67 a123 |b123 5 8 | 4 13 69 | | 89 123 58 | 4 123 6 | 7 35-9 2359 | | 123 46 45 | 7 9 123 | 8 1356 2356 | |-------------------+-------------------+-------------------| | 12 8 6 | 5 7 4 | 12 39 39 | | 4 123 7 | 9 123 123 | 6 58 58 | | 5 9 123 | 8 6 123 | 12 47 47 | |-------------------+-------------------+-------------------| | 6 5 13-2 |c123 d123 7 | 9 48 48 | | 237 237 48 |c36-2 48 9 | 5 67 1 | | 178 147 9 | 16 48 5 | 3 2 67 | *-----------------------------------------------------------*

06: 2’s abcd => r7c3<>2
07: (9=3)r4c8-r1c8=[finned X-wing:3’s r1c34,r7c3,B7]-(3=6)r8c4-r9c4=r9c9-(6=9)r1c9 => r2c8<>9, some singles

Code: Select all: *-----------------------------------------------------------* | 79 67 123 | 123 5 8 | 4 13 69 | | 89 123 8-5 | 4 123 6 | 7 35 259 | | 123 46 45 | 7 9 12-3 | 8 1356 256 | |-------------------+-------------------+-------------------| | 12 8 6 | 5 7 4 | 12 9 3 | | 4 123 7 | 9 12-3 123 | 6 58 58 | | 5 9 123 | 8 6 123 | 12 47 47 | |-------------------+-------------------+-------------------| | 6 5 13 | 123 123 7 | 9 48 48 | | 237 237 48 | 36 48 9 | 5 67 1 | | 178 147 9 | 16 48 5 | 3 2 67 | *-----------------------------------------------------------*

Note:(1|2|3)r1c4 lead to (1|2|3)r6c3&r7c5 by (1|2|3)B7&C3
07: (3)r6c6==r6c3,r1c4 => r3c6<>3
08: (5=3)r2c8-r2c5=r7c5-(3=6)r8c4-r8c8=r3c8-(46=5)r3c23 => r2c3<>5, some singles

Code: Select all: *--------------------------------------------------* | 7 6 123 | 123 5 8 | 4 13 9 | | 9 123 8 | 4 123 6 | 7 35 25 | | 123 4 5 | 7 9 12 | 8 136 26 | |----------------+----------------+----------------| | 12 8 6 | 5 7 4 | 12 9 3 | | 4 123 7 | 9 12 123 | 6 58 58 | | 5 9 123 | 8 6 123 | 12 47 47 | |----------------+----------------+----------------| | 6 5 1-3 | 123 123 7 | 9 48 48 | | 23 237 4 | 36 8 9 | 5 67 1 | | 8 17 9 | 16 4 5 | 3 2 67 | *--------------------------------------------------*

09: (3)r7c5=(3-1)r2c5=r2c2-r9c2=r7c3 => r7c3<>3, stte

coloin wrote: This has high -q2 and suexratt but 11.7 only ... maybe DoubleTrouble for y'all !

Yes, it's a bit

. Thanks for your puzzle!
totuan

by **m_b_metcalf** » Mon Sep 09, 2024 8:36 am

A curious fact: this puzzle yields also to a double backdoor. However, r8c6 is redundant. Without that clue the double backdoor no longer works, but the puzzle has a lower rating (because 9r8c6 is a hidden single)!

Code: Select all: ....584.....4.67.....79.8...86..4...4.79.....59..6....65....9.......95.1..9....2. ED=11.7/11.7/2.6 ....584.....4.67.....79.8...86..4...4.79.....59..6....65....9........5.1..9....2. ED=11.7/1.2/1.2

Yes, how we miss our friend.

Mike

The New Sudoku Players' Forum

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