The New Sudoku Players' Forum

by **eleven** » Fri Aug 27, 2021 2:20 pm

No special puzzles, but hopefully better than none.

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

by **marek stefanik** » Fri Aug 27, 2021 4:26 pm

Code: Select all: +---------------------+---------------------+---------------------+ | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | +---------------------+---------------------+---------------------+ | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | +---------------------+---------------------+---------------------+ | 39 b29 6 | 57 17 15 | 8 4 c23 | | 458 47 48 | 9 2 3 | 15 6 157 | | 35 a27 1 | 8 6 4 | 259 29 d235–7 | +---------------------+---------------------+---------------------+

(7=2)r9c2 – 2r7c2 = (2–3)r7c9 = 3r9c9 => –7r9c9, stte

by **rjamil** » Fri Aug 27, 2021 4:32 pm

Code: Select all: +-----------------+----------------+------------------+ | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | +-----------------+----------------+------------------+ | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | +-----------------+----------------+------------------+ | 39 (2)-9 6 | 57 17 15 | 8 4 (3-2) | | 458 47 48 | 9 2 3 | 15 6 157 | | 35 (7-2) 1 | 8 6 4 | 259 29 25(37)| +-----------------+----------------+------------------+

Strong Wing: SL 7 @ r9c29 3 @ r79c9 2 @ r79c2 2 @ r7c29 => -9 @ r7c2 => -2 @ r9c2 r7c9; stte

R. Jamil

by **P.O.** » Fri Aug 27, 2021 5:55 pm

Code: Select all: after singles: 4789 6 4789 1 5 2 3 489 48 1 49 489 6 3 7 2459 2489 2458 2 3 5 4 89 89 7 1 6 47 8 247 257 147 156 1246 3 9 349 5 2349 23 1489 1689 1246 7 1248 6 1 23479 237 4789 89 24 5 248 34579 2479 6 57 17 15 8 249 123457 a4-57×8 g+4-7 h-4-7+8 9 2 3 b14*5 6 b14*57 d-3+579 f2+79 1 8 6 4 c2-59 29 ec2+3-5-7 depth: 5 candidate: 8 from start ((5 0) (8 1 7) (4 5 7 8)) ((5 0 1 0) ((8 7 9) (1 4 5)) ((8 9 9) (1 4 5 7))) ((5 1 16) (9 1 7) (3 5 7 9)) ((3 2 10) (9 9 9) (2 3 5 7)) ((7 3 10) (9 2 7) (2 7 9)) ((4 4 9) (8 2 7) (4 7)) ((8 5 70) (8 3 7) (4 7 8)) ste.

by **Leren** » Fri Aug 27, 2021 8:39 pm

Code: Select all: *-----------------------------------------------* | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | |--------------+--------------+-----------------| | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | |--------------+--------------+-----------------| |b39 29 6 | 57 17 15 | 8 4 a23 | | 458 47 48 | 9 2 3 | 15 6 157 | |c35 27 1 | 8 6 4 | 259 29 d257-3 | *-----------------------------------------------*

(3=2) r7c9 - r7c2 = (2-7) r9c2 = (7) r9c9 => - 3 r9c9; stte

Leren

by **Cenoman** » Fri Aug 27, 2021 9:05 pm

Code: Select all: +---------------------+---------------------+----------------------+ | 789 6 789 | 1 5 2 | 3 b8+9 4 | | 1 49 489 | 6 3 7 | 259* 289* 25* | | 2 3 5 | 4 89 89 | 7 1 6 | +---------------------+---------------------+----------------------+ | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | +---------------------+---------------------+----------------------+ | 39 29 6 | 57 17 15 | 8 4 e3-2 | | 458 47 48 | 9 2 3 | 15 6 157 | | 35 c7+2 1 | 8 6 4 | 259* a29* d2357* | +---------------------+---------------------+----------------------+

MUG (259)r29c789 using externals
(2=9)r9c8 - (9)r1c8 == (2-7)r9c2 = (7-3)r9c9 = (3)r7c9 => -2 r7c9; ste

by **jco** » Sat Aug 28, 2021 2:27 am

Code: Select all: .---------------------------------------------------. | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | |----------------+----------------+-----------------| | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | |----------------+----------------+-----------------| | 9-3 29 6 | 57 17 15 | 8 4 b23 | | 458 47 48 | 9 2 3 | 15 6 157 | |a35 27 1 | 8 6 4 |b259 b29 2357 | '---------------------------------------------------'

(3=5)r9c1 - (5=293)b9p378 => -3 r7c1; ste

Website · by **denis_berthier** » Sat Aug 28, 2021 6:20 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 789 6 789 ! 1 5 2 ! 3 89 4 ! ! 1 49 489 ! 6 3 7 ! 259 289 25 ! ! 2 3 5 ! 4 89 89 ! 7 1 6 ! +-------------------+-------------------+-------------------+ ! 47 8 247 ! 257 147 156 ! 1246 3 9 ! ! 49 5 2349 ! 23 1489 1689 ! 1246 7 128 ! ! 6 1 23479 ! 237 4789 89 ! 24 5 28 ! +-------------------+-------------------+-------------------+ ! 39 29 6 ! 57 17 15 ! 8 4 23 ! ! 458 47 48 ! 9 2 3 ! 15 6 157 ! ! 35 27 1 ! 8 6 4 ! 259 29 2357 ! +-------------------+-------------------+-------------------+ 121 candidates.

There are lots of really 1-step solution (not using undeclared Pairs). The simplest four are:

Code: Select all: biv-chain[3]: c2n2{r7 r9} - r9n7{c2 c9} - b9n3{r9c9 r7c9} ==> r7c9≠2 stte

Code: Select all: biv-chain[3]: r7n2{c2 c9} - b9n3{r7c9 r9c9} - r9n7{c9 c2} ==> r9c2≠2 stte

Code: Select all: biv-chain[3]: r7c9{n3 n2} - b7n2{r7c2 r9c2} - r9n7{c2 c9} ==> r9c9≠3 stte

Code: Select all: biv-chain[3]: r9c2{n7 n2} - r7n2{c2 c9} - b9n3{r7c9 r9c9} ==> r9c9≠7 stte

by **RSW** » Sat Aug 28, 2021 8:43 am

Code: Select all: +--------------+--------------+---------------+ | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | +--------------+--------------+---------------+ | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | +--------------+--------------+---------------+ |b39 a29 6 | 57 17 15 | 8 4 23 | | 458 47 48 | 9 2 3 | 15 6 157 | |c35 *7-2 1 | 8 6 4 |d259 d29 2357 | +--------------+--------------+---------------+

(2=9)r7c2 - (9=3)r7c1 - (3=5)r9c1 - (5=29)r9c78 => -2r9c2; stte
I assume this is similar to Denis Berthier's 2nd biv chain, but I don't understand that terminology.

Website · by **denis_berthier** » Sat Aug 28, 2021 10:55 am

RSW wrote:
Code: Select all
+--------------+--------------+---------------+ | 789 6 789 | 1 5 2 | 3 89 4 | | 1 49 489 | 6 3 7 | 259 289 25 | | 2 3 5 | 4 89 89 | 7 1 6 | +--------------+--------------+---------------+ | 47 8 247 | 257 147 156 | 1246 3 9 | | 49 5 2349 | 23 1489 16 | 1246 7 128 | | 6 1 23479 | 237 4789 89 | 24 5 28 | +--------------+--------------+---------------+ |b39 a29 6 | 57 17 15 | 8 4 23 | | 458 47 48 | 9 2 3 | 15 6 157 | |c35 *7-2 1 | 8 6 4 |d259 d29 2357 | +--------------+--------------+---------------+

(2=9)r7c2 - (9=3)r7c1 - (3=5)r9c1 - (5=29)r9c78 => -2r9c2; stte
I assume this is similar to Denis Berthier's 2nd biv chain, but I don't understand that terminology.

It is close but not the same chain.
biv-chain[3]: r7n2{c2 c9} - b9n3{r7c9 r9c9} - r9n7{c9 c2} ==> r9c2≠2
has length 3; your chain has equivalent length 4 (in AIC notation, in case there are no inner Subsets, just count the number of = signs; in this case the end is a Subset[2]; so it counts for 2)
my biv-chain[3] uses 3 bivalue (i.e. in the present case bilocal) cells: r7n2, b9n3 and r9n7. I'm sure you can easily translate this into AIC notation.

If you want a better comparison, there is Leren's chain:
(3=2) r7c9 - r7c2 = (2-7) r9c2 = (7) r9c9 => - 3 r9c9; stte
In my notation, it's exactly:
r7c9{n3 n2} — c2n2{r7 r9} — r9n7{c2 c9} => r9c9≠3
which is close to my third chain; the only difference is, mine uses conjugacy in block b7 instead of column c2 (the two are valid).

In the nrc notation, super-symmetry is fully taken into account and there's no difference between bivalue and conjugacy; bivalue pairs/conjugate pairs always appear inside curly brackets. But, when needed, the type of CSP-Variable (or 2D-cell) before the brackets allows to know precisely what is meant.

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