The New Sudoku Players' Forum

by **Leren** » Sat Jun 26, 2021 9:21 am

Code: Select all: *-----------* |7..|.4.|1.6| |3..|.86|..7| |.16|9..|.3.| |---+---+---| |...|.7.|9..| |1.7|3..|..2| |...|2..|6.3| |---+---+---| |...|..5|..4| |...|.92|.5.| |45.|.3.|.6.| *-----------* 7...4.1.63...86..7.169...3.....7.9..1.73....2...2..6.3.....5..4....92.5.45..3..6.

by **pjb** » Sat Jun 26, 2021 11:20 am

Code: Select all: 7 289 289 | 5 4 3 | 1 289 6 3 249 2459 | 1 8 6 |a25 29 7 58 1 6 | 9 2 7 | 4 3 58 ------------------------+----------------------+--------------------- 2568 23468 23458 | 68 7 48 | 9 148 158 1 4689 7 | 3 f56 489 | 8-5 48 2 589 489 4589 | 2 15 1489 | 6 7 3 ------------------------+----------------------+--------------------- 289 23789 12389 | 678 e16 5 | 2378 128 4 68 3678 138 | 4 9 2 | 378 5 18 4 5 c128 | 78 3 d18 |b278 6 9

(5=2)r2c7 - (2)r9c7 = (2-1)r9c3 = (1)r9c6 - (1=6)r7c5 - (6=5)r5c5 => -5 r5c7; stte

Phil

by **jco** » Sat Jun 26, 2021 4:25 pm

Code: Select all: .-----------------------------------------------------. | 7 289 289 | 5 4 3 | 1 289 6 | | 3 249 249-5 | 1 8 6 |f25 29 7 | |a58 1 6 | 9 2 7 | 4 3 b58 | |--------------------+---------------+----------------| | 2568 23468 23458 |c68 7 c48 | 9 c148 c158 | | 1 4689 7 | 3 d56 489 |e58 48 2 | | 589 489 4589 | 2 15 1489 | 6 7 3 | |--------------------+---------------+----------------| | 289 23789 12389 | 678 16 5 | 2378 128 4 | | 68 3678 138 | 4 9 2 | 378 5 18 | | 4 5 128 | 78 3 18 | 278 6 9 | '-----------------------------------------------------'

(5)r3c1 = r3c9 - (5=1486)r4c4689 - (6=5)r5c5 - r5c7 = (5)r2c7 => -5 r2c3; ste

by **P.O.** » Sat Jun 26, 2021 5:03 pm

Code: Select all: 7 289 289 5 4 3 1 289 6 3 e-2+4-9 2459 1 8 6 e+2-5 e-2+9 7 58 1 6 9 2 7 4 3 58 2568 23468 23458 68 7 148 9 148 158 1 f-4-6+(89) 7 3 c-5+6 489 d+58 48 2 f+5-(89) f-4+(89) 4589 2 a-1×5 1489 6 7 3 2689 236789 12389 678 b+1-6 5 2378 128 4 68 3678 138 4 9 2 378 5 18 4 5 128 78 3 18 278 6 9 after singles. depth: 4 candidate: 5 from start ((1 0) (6 5 5) (1 5)) ((1 0) (7 5 8) (1 6)) ((6 1 10) (5 5 5) (5 6)) ((5 2 10) (5 7 6) (5 8)) ((4 3 111) (2 2 1) (2 4 9)) ((5 4 113) (6 1 4) (5 8 9))

by **Ngisa** » Sat Jun 26, 2021 9:50 pm

Code: Select all: +------------------------+-------------------+-----------------+ | 7 289 289 | 5 4 3 | 1 289 6 | | 3 249 2459 | 1 8 6 |h5-2 29 7 | | 58 1 6 | 9 2 7 | 4 3 58 | +------------------------+-------------------+-----------------+ | 2568 23468 23458 | 68 7 48 | 9 148 158 | | 1 4689 7 | 3 f56 489 | g58 48 2 | | 589 489 4589 | 2 e15 d1489 | 6 7 3 | +------------------------+-------------------+-----------------+ | 289 23789 12389 | 678 16 5 | 2378 128 4 | | 68 3678 138 | 4 9 2 | 378 5 18 | | 4 5 b128 | 78 3 c18 |a278 6 9 | +------------------------+-------------------+-----------------+

(2)r9c7 = (2-1)r9c3 = r9c6 - r6c6 = (1-5)r6c5 = r5c5 - r5c7 = (5)r2c7 => - 2r2c7; stte

Clement

Website · by **denis_berthier** » Mon Jun 28, 2021 5:05 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 7 289 289 ! 5 4 3 ! 1 289 6 ! ! 3 249 2459 ! 1 8 6 ! 25 29 7 ! ! 58 1 6 ! 9 2 7 ! 4 3 58 ! +-------------------+-------------------+-------------------+ ! 2568 23468 23458 ! 68 7 48 ! 9 148 158 ! ! 1 4689 7 ! 3 56 489 ! 58 48 2 ! ! 589 489 4589 ! 2 15 1489 ! 6 7 3 ! +-------------------+-------------------+-------------------+ ! 289 23789 12389 ! 678 16 5 ! 2378 128 4 ! ! 68 3678 138 ! 4 9 2 ! 378 5 18 ! ! 4 5 128 ! 78 3 18 ! 278 6 9 ! +-------------------+-------------------+-------------------+

===> There are 19 W1-anti-backdoors:
n8r1c8 n4r2c2 n5r2c3 n2r2c7 n8r3c1 n5r3c9 n8r4c4 n4r4c6 n6r5c5 n5r5c7 n5r6c5 n1r6c6 n6r7c4 n1r7c5 n2r7c8 n1r9c3 n7r9c4 n8r9c6 n2r9c7
15 of which give rise to a 1-^step solution with whips[≤6]

The simplest 6 need only a bivalue-chain[5]:

Code: Select all: biv-chain[5]: r9n2{c7 c3} - r9n1{c3 c6} - b5n1{r6c6 r6c5} - b5n5{r6c5 r5c5} - c7n5{r5 r2} ==> r2c7 ≠ 2 stte

OR:

Code: Select all: biv-chain[5]: r7c5{n6 n1} - r9n1{c6 c3} - r9n2{c3 c7} - r2c7{n2 n5} - r5n5{c7 c5} ==> r5c5 ≠ 6 stte

OR:

Code: Select all: biv-chain[5]: r2c7{n5 n2} - r9n2{c7 c3} - r9n1{c3 c6} - b5n1{r6c6 r6c5} - b5n5{r6c5 r5c5} ==> r5c7 ≠ 5 stte

OR:

Code: Select all: biv-chain[5]: r5n5{c5 c7} - r2c7{n5 n2} - r9n2{c7 c3} - r9n1{c3 c6} - b5n1{r6c6 r6c5} ==> r6c5 ≠ 5 stte

OR:

Code: Select all: biv-chain[5]: r6c5{n1 n5} - r5n5{c5 c7} - r2c7{n5 n2} - r9n2{c7 c3} - r9n1{c3 c6} ==> r6c6 ≠ 1, r7c5 ≠ 1 stte

OR:

Code: Select all: biv-chain[5]: r9n2{c3 c7} - r2c7{n2 n5} - r5n5{c7 c5} - c5n6{r5 r7} - b8n1{r7c5 r9c6} ==> r9c3 ≠ 1 stte

by **Sudtyro2** » Mon Jun 28, 2021 9:26 pm

Code: Select all: +---------------------+-----------------+--------------- | 7 289 289 | 5 4 3 | 1 289 6 | | 3 249 2459 | 1 8 6 | c25 29 7 | | 58 1 6 | 9 2 7 | 4 3 58 | +---------------------+-----------------+---------------+ | 2568 23468 23458 | 68 7 48 | 9 148 158 | | 1 4689 7 | 3 e56 489 | d58 48 2 | | 589 489 4589 | 2 f15 *489-1 | 6 7 3 | +---------------------+-----------------+---------------+ | 289 23789 12389 | 678 *6-1 5 | 2378 128 4 | | 68 3678 138 | 4 9 2 | 378 5 18 | | 4 5 a*128# | 78 3 *18 | b278 6 9 | +---------------------+-----------------+---------------+

Examples regarding potential issues (IMO) about notation standards...

(*)Siamese Kraken Franken 1x1 Fish(1)r9\(b8,c6) + rfr9c3(#):
(1-2)r9c3 = r9c7 - (2=5)r2c7 - r5c7 = r5c5 - (5=1)r6c5 => -1 r6c6,r7c5; ste

Or, simply start the chain with (1)r9c6 for the more familiar Kraken (1)r9c36:
(1)r9c6 = (1-2)r9c3 = r9c7 - (2=5)r2c7 - r5c7 = r5c5 - (5=1)r6c5 => -1 r6c6,r7c5; ste

As explained by SpAce here, the Siamese 1-Fish cover notation (b8,c6) is a necessary complication due to the two separate covers available to provide the double elimination. Except for that, the notation clearly follows standard UFG guidelines.

The two XY chains shown above use standard Eureka notation comprising leading digit(s) adjacent to their row/column positions (same digits need not be repeated).

On the other hand, postings to date by P.O. use a totally unfamiliar notation, at least for me. I think some recent changes have been made to the main puzzle board, but everything else below the "depth" level is a mystery. I look forward to more complete explanations of the notation conventions.

I did also find it interesting that denis_berthier's posting on this same puzzle used two separate "bi-value" chains to reproduce the two eliminations generated by the 1-Fish or by the Kraken cell approach. However, I'm not familiar with the chain notation used although I can with effort slowly translate it to Eureka format where "bi-value" refers only to a 2-digit cell.

SteveC

by **eleven** » Mon Jun 28, 2021 10:32 pm

If you want to understand P.O.'s notation just concentrate on the first column, which gives the digit, and the first 2 within the next brackets, which give the row and column.
Either the digit is true, that is stated in the first line, or the following lines are true.
In that sample:
1r6c5 = (1-6*)r7c5 = (6-5)r5c5 = r5c8 - (5=294)r2c892 - (4=*895)b4p487 => -5r6c5

Note that those chains are remembering all eliminatins on the way.

(Neither notation nor chain are my favourites - Denis lists a bivalue chain for the same elimination, but the marking in the grid is really helpful)

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