The New Sudoku Players' Forum

Website · by **denis_berthier** » Fri Jun 16, 2023 4:43 am

.
As I'm slowly reaching the end of the 158,276 puzzles in mith's T&E(3) min-expand list, I have no really new findings (the effect of adding various subsets of impossible patterns remain similar to what I reported about the first slices of the list.
Here's a typical puzzle that requires no extra impossible pattern.

Code: Select all: +-------+-------+-------+ ! 1 . 3 ! . . 6 ! . . 9 ! ! . 5 7 ! 1 . 9 ! . . 6 ! ! 6 9 . ! 3 . . ! . . . ! +-------+-------+-------+ ! . . . ! . . 5 ! 8 9 . ! ! . . 9 ! . . . ! . 6 7 ! ! . . . ! . . . ! 4 2 . ! +-------+-------+-------+ ! 3 6 . ! 5 . 1 ! . 7 . ! ! . 7 1 ! . . . ! . . . ! ! 9 . 5 ! . . 7 ! 6 1 . ! +-------+-------+-------+ 1.3..6..9.571.9..669.3..........589...9....67......42.36.5.1.7..71......9.5..761.;37795;701910 SER = 10.4

Code: Select all: Resolution state after Singles (and whips[1]): +----------------------+----------------------+----------------------+ ! 1 248 3 ! 2478 24578 6 ! 257 458 9 ! ! 248 5 7 ! 1 248 9 ! 23 348 6 ! ! 6 9 248 ! 3 24578 248 ! 1257 458 12458 ! +----------------------+----------------------+----------------------+ ! 247 1234 246 ! 2467 123467 5 ! 8 9 13 ! ! 2458 12348 9 ! 248 12348 2348 ! 135 6 7 ! ! 578 138 68 ! 6789 136789 38 ! 4 2 135 ! +----------------------+----------------------+----------------------+ ! 3 6 248 ! 5 2489 1 ! 29 7 248 ! ! 248 7 1 ! 24689 234689 2348 ! 2359 3458 23458 ! ! 9 248 5 ! 248 2348 7 ! 6 1 2348 ! +----------------------+----------------------+----------------------+ 178 candidates.

by **pjb** » Sat Jun 17, 2023 1:29 am

Lots of TH's (total of 11)

type 3 TH with 7 at r1c4, 9 at r7c5 and at r8c6

Code: Select all: 1 248* 3 | 248*7 24578 6 | 257 458 9 248* 5 7 | 1 248* 9 | 23 348 6 6 9 248* | 3 24578 248* | 1257 458 12458 ------------------------+----------------------+--------------------- 247 1234 246 | 2467 123467 5 | 8 9 13 2458 12348 9 | 248 12348 2348 | 135 6 7 578 138 68 | 6789 136789 38 | 4 2 135 ------------------------+----------------------+--------------------- 3 6 248* | 5 248*9 1 | 29 7 248 248* 7 1 | 24689 234689 248*3 | 2359 3458 23458 9 248* 5 | 248* 2348 7 | 6 1 2348

1.
chain1: (7)r1c4 - r1c5
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = (2-1)r3c9 = (1-7)r3c7 = r3c5 - r1c5
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - r3c9 = (1-7)r3c7 = r1c7 - r1c5 => -7 r1c5;

2.
chain1: (7)r1c4 - r1c7 = (7-2)r3c7
chain2: (9)r7c5 - r6c5 = r6c4 - r8c4 = r8c7 - (9=2)r7c7 - r3c7
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - r3c9 = (1-2)r3c7 => -2 r3c7;

3.
chain1: (7)r1c4 - r1c7 = (7-5)r3c7
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = (2-1)r3c9 = (1-5)r3c7
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - r3c9 = (1-5)r3c7 => -5 r3c7;

4.
chain1: (7)r1c4 - r1c7 = (7-1)r3c7 = (1-5)r3c9
chain2: (9)r7c5 - r6c5 = r6c4 - r8c4 = r8c7 - (9=2)r7c7 - r1c7 = (2-5)r3c9
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - (13=5)r6c9 - r3c9 => -5 r3c9

5.
chain1: (7)r1c4 - r1c7 = (7-1)r3c7 = r3c9 - (1=3)r4c9 - (13=5)r6c9 - r6c1 = (5-2)r5c1
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = r3c9 - r3c3 = r4c3 - r5c1
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - (13=5)r6c9 - r6c1 = (5-2)r5c1 => -2 r5c1

6.
chain1: (7)r1c4 - r1c7 = (7-1)r3c7 = r3c9 - (1=3)r4c9 - r8c9
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = r3c9 - (2=3)r2c7 - r2c8 = r8c8 - r8c9
chain3: (3)r8c6 - r8c7 = r9c9 - r8c9 => -3 r8c9;

7.
chain1: (7)r1c4 - r1c7 = (7-1)r3c7 = r3c9 - (1=3)r4c9 - r9c9 = r9c5 - r5c5
chain2: (9)r7c5 - (9=2)r7c7 - (2=3)r2c7 - r2c8 = r8c8 - r8c6 = r9c5 - r5c5
chain3: (3)r8c6 - r8c7 = r9c9 - (3=1)r4c9 - (13=5)r6c9 - (15=3)r5c7 - r5c5 => -3 r5c5

8.
chain1: (7)r1c4 - r1c7 = (7-1)r3c7 = r3c9 - (1=3)r4c9 - r9c9 = r9c5 - r8c5
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = r3c9 - (2=3)r2c7 - r2c8 = r8c8 - r8c5
chain3: (3)r8c6 - r8c5 => -3 r8c5

State after above:

Code: Select all: 1 248 3 | 2478 2458 6 | 257 458 9 248 5 7 | 1 248 9 | 23 348 6 6 9 248 | 3 24578 248 | 17 458 1248 ------------------------+----------------------+--------------------- 247 1234 246 | 2467 123467 5 | 8 9 13 458 12348 9 | 248 1248 2348 | 135 6 7 578 138 68 | 6789 136789 38 | 4 2 135 ------------------------+----------------------+--------------------- 3 6 248 | 5 2489 1 | 29 7 248 248 7 1 | 24689 24689 2348 | 2359 3458 2458 9 248 5 | 248 2348 7 | 6 1 2348

then:

(8=7)r159c4 - (7=1)r12578c7 - (1=8)r5c456, r6c6 => -2 r4c4, -4 r4c4, -8 r6c4

9.
type 3 TH with 7 at r1c4, 9 at r7c5 and at 3 at r8c6
chain1: (7)r1c4 - (7=6)r4c4 - r4c3
chain2: (9)r7c5 - (9=2)r7c7 - r1c7 = r3c9 - r3c3 = (2-6)r4c3
chain3: (3)r8c6 - (3=8)r6c6 - (8=6)r6c3 - r4c3 => -6 r4c3;

Then kraken row 8:
chain1: (9)r8c4 - (9=7)r6c4 - r1c4
chain2: (9-6)r8c5 = r4c5 - (6=7)r4c4 - r1c4
chain3: (9)r8c7 - (9=2)r7c7 - r1c7 = (2-1)r3c9 = (1-7)r3c7 = r3c5 - r1c4 => -7 r1c4;

Naked triplets of 248 at r159c4 => -2 r8c4, -4 r8c4, -8 r8c4

10.
type 2 TH with SL between 9 at r7c5 and 3 at r8c6
Continuous chain: (9)r7c5 = (3)r8c6 - (3)r8c8 = (3)r2c8 - (3=2)r2c7 - (2=9)r7c7 - loop => -3 r8c7; -2 r8c7;

11.
type 2 TH with SL between 9 at r7c5 and 3 at r8c6
chain1: (9)r7c5 - r6c5 = r6c4 - (9=6)r8c4 - (6=7)r4c4 - r4c1 = (7-5)r6c1
chain2: (3)r8c6 - r8c8 = r9c9 - (3=1)r4c9 - (13=5)r6c9 - r6c1 => -5 r6c1;

2s at r79c5 only ones in row/column => -2 r9c4.
8s at r9c45 only ones in row/column => -8 r7c5.

Leading to:

Code: Select all: 1 24 3 | 248 5 6 | 7 48 9 48 5 7 | 1 48 9 | 2 3 6 6 9 248 | 3 7 24 | 1 5 48 ------------------------+----------------------+--------------------- 24 3 24 | 7 6 5 | 8 9 1 5 8 9 | 24 1 24 | 3 6 7 7 1 6 | 9 3 8 | 4 2 5 ------------------------+----------------------+--------------------- 3 6 248 | 5 24 1 | 9 7 248 248 7 1 | 6 9 3 | 5 48 248 9 24 5 | 48 248 7 | 6 1 3

Then (2=4)r1c2 - (4=8)r1c8 - (8=4)r3c9 - (4=2)r3c6 => -2 r1c4, r3c3; stte

Phil

by **Cenoman** » Sat Jun 17, 2023 3:39 pm

At the initial resolution state, note TH(248)b1289 having three guardians (7r1c4, 9r7c5, 8r8c6)

Code: Select all: +-----------------------+----------------------------+--------------------------+ | 1 248* 3 | Aa2478* 24578 6 | Bb257 B458 9 | | 248* 5 7 | 1 248* 9 | B23 B348 6 | | 6 9 248* | 3 24578 248* | c1257 B458 12458 | +-----------------------+----------------------------+--------------------------+ | 247 1234 246 | 67-24 123467 5 | 8 9 13 | | 2458 12348 9 | Aea248 e12348 e2348 | d135 6 7 | | 578 138 68 | 679-8 136789 e38 | 4 2 135 | +-----------------------+----------------------------+--------------------------+ | 3 6 248* | 5 2489* 1 | C29 7 248 | | 248* 7 1 | E69-248 E234689 2348* | D2359 3458 23458 | | 9 248* 5 | Aa248* 2348 7 | 6 1 2348 | +-----------------------+----------------------------+--------------------------+

1. (248=7)r159c4 - r1c7 = (7-1)r3c7 = r5c7 - (1=2348)b5p4569 => -24 r4c4, -8 r6c4
2. (248=7)r159c4 - (7=34582)b3p12458 - (2=9)r7c7 - r8c7 = (96)r8c45 => -248 r8c4; lcls (eliminating 7r1c4, r46c5)

Code: Select all: +-----------------------+------------------------+------------------------+ | 1 248 3 | 248 57 6 | 257 458 9 | | 248 5 7 | 1 248 9 | B23 348 6 | | 6 9 248 | 3 57 248 | b1257 458 c12458 | +-----------------------+------------------------+------------------------+ | 247 1234 246 | 67 12346 5 | 8 9 13 | | 2458 12348 9 | 248 12348 2348 |Aa135w 6 7 | | y578 138 68 | y679 z13689 38 | 4 2 x135 | +-----------------------+------------------------+------------------------+ | 3 6 248 | 5 248-9 1 |Be29 7 d248 | | 248 7 1 | 69 234689 2348 | 2359 3458 d23458 | | 9 248 5 | 248 2348 7 | 6 1 d2348 | +-----------------------+------------------------+------------------------+

3. Kraken cell (135)r5c7
(1)r5c7 - r3c7 = (1-2)r3c9 = r789c9 - (2=9)r7c7
(3)r5c7 - (3=29)r27c7
(5)r5c7 - r6c9 = (57-9)r6c14 = (9)r6c5
=> -9 r7c5; 1 placement

Code: Select all: +-----------------------+-----------------------+------------------------+ | 1 248* 3 | 248* 57 6 | 257 458 9 | | 248* 5 7 | 1 248* 9 | 23 348 6 | | 6 9 248* | 3 57 248* | 1257 458 12458 | +-----------------------+-----------------------+------------------------+ | 247 1234 246 | 67 12346 5 | 8 9 13 | | 2458 12348 9 | 248 12348 2348 | 135 6 7 | | 578 138 68 | 679 13689 38 | 4 2 135 | +-----------------------+-----------------------+------------------------+ | 3 6 248* | 5 248* 1 | 9 7 248 | | 248* 7 1 | 69 234689 248+3* | 235 3458 23458 | | 9 248* 5 | 248* 2348 7 | 6 1 2348 | +-----------------------+-----------------------+------------------------+

4. TH(248)b1289 has now a single guardian => +3 r8c6; 27 placements

Code: Select all: +-------------------+-------------------+------------------+ | 1 a24 3 | 48-2 5 6 | 7 b48 9 | | 48 5 7 | 1 48 9 | 2 3 6 | | 6 9 48-2 | 3 7 d24 | 1 5 c48 | +-------------------+-------------------+------------------+ | 24 3 24 | 7 6 5 | 8 9 1 | | 5 8 9 | 24 1 24 | 3 6 7 | | 7 1 6 | 9 3 8 | 4 2 5 | +-------------------+-------------------+------------------+ | 3 6 248 | 5 248 1 | 9 7 248 | | 248 7 1 | 6 9 3 | 5 48 248 | | 9 24 5 | 248 248 7 | 6 1 3 | +-------------------+-------------------+------------------+

5. W-Wing (2=4)r1c2 - r1c8 = r3c9 - (4=2)r3c6 => -2 r3c3, r1c4; ste

by **ghfick** » Sun Jun 18, 2023 2:23 am

Consider column 2 and {2,4,8}. r1459c2 has 4 guardians.
Also column 5 and {2,4,8}. r2357c5 has 4 guardians or r1257c5 has 4 guardians.
YZF_Sudoku gives forcing chains for each of these 'impossible patterns'. None are 'easy'.
Do these patterns have another name? Not at all like TH.

Website · by **denis_berthier** » Sun Jun 18, 2023 4:30 am

.
Since when is a quad an impossible pattern? As there's no impossible pattern, there's nothing to guard against.
.

Website · by **denis_berthier** » Sun Jun 18, 2023 4:38 am

.
Hi pjb, Cenoman

My resolution path is similar to yours. First use the tridagon with 3 guardians and then with 1 (and with 2 in the middle)

Using ORk-whips instead of ORk-forcing-whips allows shorter chains (6 instead of 8).

Code: Select all: t-whip[2]: r9n3{c5 c9} - b6n3{r6c9 .} ==> r5c5≠3 Trid-OR3-relation for digits 2, 4 and 8 in blocks: b1, with cells (marked #): r1c2, r2c1, r3c3 b2, with cells (marked #): r1c4, r2c5, r3c6 b7, with cells (marked #): r9c2, r8c1, r7c3 b8, with cells (marked #): r9c4, r8c6, r7c5 with 3 guardians (in cells marked @): n7r1c4 n9r7c5 n3r8c6 +----------------------+----------------------+----------------------+ ! 1 248# 3 ! 2478#@ 24578 6 ! 257 458 9 ! ! 248# 5 7 ! 1 248# 9 ! 23 348 6 ! ! 6 9 248# ! 3 24578 248# ! 1257 458 12458 ! +----------------------+----------------------+----------------------+ ! 247 1234 246 ! 2467 123467 5 ! 8 9 13 ! ! 2458 12348 9 ! 248 1248 2348 ! 135 6 7 ! ! 578 138 68 ! 6789 136789 38 ! 4 2 135 ! +----------------------+----------------------+----------------------+ ! 3 6 248# ! 5 2489#@ 1 ! 29 7 248 ! ! 248# 7 1 ! 24689 234689 2348#@ ! 2359 3458 23458 ! ! 9 248# 5 ! 248# 2348 7 ! 6 1 2348 ! +----------------------+----------------------+----------------------+ z-chain[5]: r8n6{c5 c4} - b8n9{r8c4 r7c5} - r7c7{n9 n2} - r2c7{n2 n3} - c8n3{r2 .} ==> r8c5≠3

Trid-OR3-whip[6]: b6n3{r6c9 r5c7} - c7n1{r5 r3} - c7n7{r3 r1} - OR3{{n7r1c4 n3r8c6 | n9r7c5}} - r7c7{n9 n2} - r2c7{n2 .} ==> r8c9≠3
Trid-OR3-whip[6]: r6n9{c4 c5} - OR3{{n9r7c5 n7r1c4 | n3r8c6}} - b9n3{r8c7 r9c9} - r6n3{c9 c2} - r6n1{c2 c9} - r4c9{n1 .} ==> r6c4≠7

Code: Select all: biv-chain[4]: r3n1{c9 c7} - r3n7{c7 c5} - r6n7{c5 c1} - r6n5{c1 c9} ==> r6c9≠1, r3c9≠5 biv-chain[4]: c7n1{r5 r3} - r3n7{c7 c5} - r6n7{c5 c1} - b4n5{r6c1 r5c1} ==> r5c7≠5 singles ==> r6c9=5, r5c1=5 biv-chain[3]: c9n1{r3 r4} - b6n3{r4c9 r5c7} - r2c7{n3 n2} ==> r3c9≠2 whip[1]: c9n2{r9 .} ==> r7c7≠2, r8c7≠2 naked-single ==> r7c7=9 +----------------------+----------------------+----------------------+ ! 1 248 3 ! 2478 24578 6 ! 257 458 9 ! ! 248 5 7 ! 1 248 9 ! 23 348 6 ! ! 6 9 248 ! 3 24578 248 ! 1257 458 148 ! +----------------------+----------------------+----------------------+ ! 247 1234 246 ! 2467 123467 5 ! 8 9 13 ! ! 5 12348 9 ! 248 1248 2348 ! 13 6 7 ! ! 78 138 68 ! 689 136789 38 ! 4 2 5 ! +----------------------+----------------------+----------------------+ ! 3 6 248 ! 5 248 1 ! 9 7 248 ! ! 248 7 1 ! 24689 24689 2348 ! 35 3458 248 ! ! 9 248 5 ! 248 2348 7 ! 6 1 2348 ! +----------------------+----------------------+----------------------+ At least one candidate of a previous Trid-OR3-relation between candidates n7r1c4 n9r7c5 n3r8c6 has just been eliminated. There remains a Trid-OR2-relation between candidates: n7r1c4 n3r8c6 hidden-pairs-in-a-block: b8{n6 n9}{r8c4 r8c5} ==> r8c5≠8, r8c5≠4, r8c5≠2, r8c4≠8, r8c4≠4, r8c4≠2

Trid-OR2-whip[3]: r8c7{n5 n3} - OR2{{n3r8c6 | n7r1c4}} - c7n7{r1 .} ==> r3c7≠5
t-whip[4]: r6n3{c6 c2} - r6n1{c2 c5} - c5n9{r6 r8} - c5n6{r8 .} ==> r4c5≠3
biv-chain[4]: b6n1{r5c7 r4c9} - c9n3{r4 r9} - c5n3{r9 r6} - r6n1{c5 c2} ==> r5c2≠1
Trid-OR2-whip[4]: r3n7{c7 c5} - OR2{{n7r1c4 | n3r8c6}} - c8n3{r8 r2} - r2c7{n3 .} ==> r3c7≠2
z-chain[5]: c5n9{r6 r8} - c5n6{r8 r4} - c5n1{r4 r5} - c7n1{r5 r3} - r3n7{c7 .} ==> r6c5≠7
hidden-single-in-a-row ==> r6c1=7
Trid-OR2-whip[4]: r4c9{n1 n3} - r9n3{c9 c5} - OR2{{n3r8c6 | n7r1c4}} - r4n7{c4 .} ==> r4c5≠1

Code: Select all: hidden-pairs-in-a-row: r4{n1 n3}{c2 c9} ==> r4c2≠4, r4c2≠2 biv-chain[4]: c5n3{r6 r9} - c9n3{r9 r4} - r4n1{c9 c2} - r6n1{c2 c5} ==> r6c5≠6, r6c5≠8, r6c5≠9 singles ==> r6c4=9, r8c4=6, r8c5=9, r4c5=6, r6c3=6, r4c4=7 +-------------------+-------------------+-------------------+ ! 1 248 3 ! 248 24578 6 ! 257 458 9 ! ! 248 5 7 ! 1 248 9 ! 23 348 6 ! ! 6 9 248 ! 3 24578 248 ! 17 458 148 ! +-------------------+-------------------+-------------------+ ! 24 13 24 ! 7 6 5 ! 8 9 13 ! ! 5 2348 9 ! 248 1248 2348 ! 13 6 7 ! ! 7 138 6 ! 9 13 38 ! 4 2 5 ! +-------------------+-------------------+-------------------+ ! 3 6 248 ! 5 248 1 ! 9 7 248 ! ! 248 7 1 ! 6 9 2348 ! 35 3458 248 ! ! 9 248 5 ! 248 2348 7 ! 6 1 2348 ! +-------------------+-------------------+-------------------+ At least one candidate of a previous Trid-OR2-relation between candidates n7r1c4 n3r8c6 has just been eliminated. There remains a Trid-OR1-relation between candidates: n3r8c6

Trid-ORk-relation with only one candidate => r8c6=3

The end is easy, in BC3.

by **totuan** » Sun Jun 18, 2023 9:04 am

ghfick wrote:Consider column 2 and {2,4,8}. r1459c2 has 4 guardians.
Also column 5 and {2,4,8}. r2357c5 has 4 guardians or r1257c5 has 4 guardians.
YZF_Sudoku gives forcing chains for each of these 'impossible patterns'. None are 'easy'.
Do these patterns have another name? Not at all like TH.

Code: Select all: *-----------------------------------------------------------------------------* | 1 *248 3 | 2478 24578 6 | 257 458 9 | | 248 5 7 | 1 #248 9 | 23 348 6 | | 6 9 248 | 3 #24578 248 | 1257 458 12458 | |-------------------------+-------------------------+-------------------------| | 247 *1234 246 | 2467 123467 5 | 8 9 13 | | 2458 *12348 9 | 248 #12348 2348 | 135 6 7 | | 578 138 68 | 6789 136789 38 | 4 2 135 | |-------------------------+-------------------------+-------------------------| | 3 6 248 | 5 #2489 1 | 29 7 248 | | 248 7 1 | 24689 234689 2348 | 2359 3458 23458 | | 9 *248 5 | 248 2348 7 | 6 1 2348 | *-----------------------------------------------------------------------------*

It seems:
DP(248)r1459c2 * marked cells => 4 guardians (13)r45c2
DP(248)r2357c5 # marked cells => 5 guardians (57)r3c5, (13)r5c5, (9)r7c5
I don’t use YZF solver, so don’t know what eliminated are?

totuan

by **DEFISE** » Sun Jun 18, 2023 10:36 am

Tridagon with 3 guardians : 7r1c4, 9r7c5, 3r8c6
No initial basics.
S3-whip[9]: r3n7{c5 c7}- c7n1{r3 r5}- c5{r5n1 HT: r468n167}- c5n9{r6 r7}- r7c7{n9 n2}- c9n2{r7 r3}- r3n1{c9 .} => -7r1c4

2 guardians remaining : 9r7c5, 3r8c6

Box/Line: 7c4b5 => -7r4c5 -7r6c5
Hidden pairs: 57c5r13 => -2r1c5 -4r1c5 -8r1c5 -2r3c5 -4r3c5 -8r3c5
Naked triplets: 248c4r159 => -2r4c4 -4r4c4 -8r6c4 -2r8c4 -4r8c4 -8r8c4

whip[8]: r6n9{c5 c4}- r8n9{c4 c7}- r7c7{n9 n2}- r2c7{n2 n3}- c8n3{r2 r8}- r8n5{c8 c9}- r6n5{c9 c1}- r6n7{c1 .} => -9r7c5

1 guardian remaining : 3r8c6 => +3r8c6

Single(s): 8r6c6, 6r6c3, 9r7c7, 3r9c9, 1r4c9, 5r6c9, 3r5c7, 2r2c7, 7r6c1, 9r6c4, 6r8c4, 7r4c4, 5r8c7, 7r1c7, 5r1c5, 7r3c5, 1r3c7, 3r2c8, 5r3c8, 6r4c5, 3r4c2, 1r6c2, 3r6c5, 1r5c5, 5r5c1, 8r5c2, 9r8c5
whip[3]: r2c5{n4 n8}- r1n8{c4 c8}- r3c9{n8 .} => -4r3c6
STTE

by **ghfick** » Sun Jun 18, 2023 12:25 pm

Hi Totuan,

First exclude r5c5 <>3 with:
Empty Rectangle : 3 in b6 connected by r9 => r5c5 <> 3

Then, there are four distinct forcing chains as noted by YZF_Sudoku

1) Impossible Pattern(248{r1257c5}) Forcing Chain: Each true guardian of Impossible Pattern will all lead to: r1c5<>8
5r1c5
7r1c5
1r5c5 - (1=23597)r12578c7 - (7=2485)b2p1259
9r7c5 - (9=2)r7c7 - (2=34587)b3p12458 - (7=2485)b2p1259

2) Impossible Pattern(248{r2357c5}) Forcing Chain: Each true guardian of Impossible Pattern will all lead to: r3c5<>2
5r3c5
7r3c5
1r5c5 - (1=23597)r12578c7 - 7r3c7 = 7r3c5
9r7c5 - (9=2)r7c7 - 2r789c9 = 2r3c9

3) Impossible Pattern(248{r2357c5}) Forcing Chain: Each true guardian of Impossible Pattern will all lead to: r3c5<>2,r3c5<>4,r3c5<>8
5r3c5
7r3c5
1r5c5 - (1=23597)r12578c7 - 7r3c7 = 7r3c5
9r7c5 - (9=2)r7c7 - (2=34587)b3p12458 - 7r3c7 = 7r3c5

4) Impossible Pattern(248{r1459c2}) Forcing Chain: Each true guardian of Impossible Pattern will all lead to: r4c5<>3
1r4c2 - (1=3)r4c9
3r4c2
1r5c2 - (1=2483)b5p4569
3r5c2 - 3r5c7 = 3r46c9 - 3r9c9 = 3r9c5

Gordon

by **totuan** » Sun Jun 18, 2023 4:27 pm

Hi Gordon,
Yes. IMO, they are “DP - deadly pattern”. The lower level of impossible patterns

.

totuan

Website · by **denis_berthier** » Sun Jun 18, 2023 6:14 pm

totuan wrote: IMO, they are “DP - deadly pattern”. The lower level of impossible patterns .

A deadly pattern is not an impossible pattern (at any high or low level). It's a pattern that implies multiple solutions.

Website · by **denis_berthier** » Mon Jun 19, 2023 2:48 am

DEFISE wrote:S3-whip[9]: r3n7{c5 c7}- c7n1{r3 r5}- c5{r5n1 HT: r468n167}- c5n9{r6 r7}- r7c7{n9 n2}- c9n2{r7 r3}- r3n1{c9 .} => -7r1c4

Good 1st step that opens the way to a short solution.

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#142195 in 158276 T&E(3) min-expands

#142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands

Re: #142195 in 158276 T&E(3) min-expands