The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..1|.2.|.34|
 |..4|7..|2..|
 |...|1..|7.6|
 |---+---+---|
 |2..|.74|..8|
 |...|...|...|
 |3..|65.|..7|
 |---+---+---|
 |4.3|..9|...|
 |..2|..7|5..|
 |51.|.3.|6..|
 *-----------*


Play/Print this puzzle online

[Leren]

Extended S wing: 3r4c4 - r4c7 = r5c7; 9r4c4 - r1c4 = r1c7 - r6c7 = 4r6c7 - r5c7; => r5c7<49>

[daj95376]

Extended S wing: 3r4c4 - r4c7 = r5c7; 9r4c4 - r1c4 = r1c7 - r6c7 = 4r6c7 - r5c7; => r5c7<49>

I get r5c7<>4 from your forcing chains. Still, it cracks the puzzle.

[Leren]

Hi daj,

The first chain => r5c7 = 3 and the second => r1c7 = 9 and r6c7 = 4, in both cases r5c7 <49>

r5c7 <> 9 is the inference from the "standard" S wing and r5c7 <> 4 follows from the "extension" bi-value cell r6c7.

Can my forcing chain notation can be improved to make this clearer ?

Leren

[ArkieTech]

These "almost xy-wings" are powerful.

Code: Select all

 *-----------------------------------------------------------*
 | 7     56    1     |b89    2     56    |a89    3     4     |
 | 689   3     4     | 7     89    56    | 2     589   1     |
 | 89    2     589   | 1     4     3     | 7     589   6     |
 |-------------------+-------------------+-------------------|
 | 2     59    569   |b39    7     4     |c139  c169   8     |
 | 1     479   679   | 2389  89    28    | 34-9 c69    5     |
 | 3     489   89    | 6     5     1     | 4-9   2     7     |
 |-------------------+-------------------+-------------------|
 | 4     678   3     | 5     16    9     | 18    178   2     |
 | 689   689   2     | 48    16    7     | 5     148   3     |
 | 5     1     78    | 248   3     28    | 6     478   9     |
 *-----------------------------------------------------------*
als xy-wing
(9=8)r1c7-(8=3)r14c4-(3=nt:169)r4c78,r5c8 => -9r56c7; stte

[daj95376]

The first chain => r5c7 = 3 and the second => r1c7 = 9 and r6c7 = 4, in both cases r5c7 <49>

r5c7 <> 9 is the inference from the "standard" S wing and r5c7 <> 4 follows from the "extension" bi-value cell r6c7.

Can my forcing chain notation can be improved to make this clearer ?

Hello Leren,

Okay, you're using an intermediate condition to "carry forward" an elimination. I would write ...

Code: Select all

original : 3r4c4 - r4c7 = r5c7; 9r4c4 - r1c4 = r1c7 - r6c7 = 4r6c7 - r5c7; => r5c7<49>

tweaked  : 3r4c4 - r4c7 = r5c7; 9r4c4 - r1c4 = r1c7* - r6c7 = 4r6c7 - r5c7; => r5c7<*94>


one chain: (3)r5c7 = r4c7 - (3=9)r4c4 - r1c4 = r1c7* - (9=4)r6c7 => r5c7<>*94


Regards, Danny

[Marty R.]

I couldn't find the one-stepper.

R5c8=9-->r4c3=6; r4c8, r5c3<>6
XY-Wing (79-8), pivot r5c3, with three transports; r7c2<>8

[denis_berthier]

Can my forcing chain notation can be improved to make this clearer ?

Hi Leren,
I suggest you have a look at the nrc notation.
But in the present puzzle, no forcing chain is necessary, whips (and the special case of bivalue-chains, i.e. basic NLs or AICs) are enough.

***** SudoRules 16.2 based on CSP-Rules 1.2, config: gW *****
singles ==> r8c9 = 3, r7c4 = 5, r5c1 = 1, r6c6 = 1, r6c8 = 2, r7c9 = 2, r9c9 = 9, r5c9 = 5, r2c9 = 1, r1c1 = 7, r3c5 = 4, r3c2 = 2, r2c2 = 3, r3c6 = 3
whip[1]: c7n4{r6 .} ==> r5c8 <> 4
whip[1]: r6n8{c3 .} ==> r5c2 <> 8, r5c3 <> 8
whip[1]: c3n6{r5 .} ==> r4c2 <> 6, r5c2 <> 6, r2c5 <> 6
biv-chain[2]: b8n6{r7c5 r8c5} - c5n1{r8 r7} ==> r7c5 <> 8
biv-chain[2]: r5c5{n8 n9} - r2c5{n9 n8} ==> r8c5 <> 8
biv-chain[2]: b2n6{r1c6 r2c6} - c6n5{r2 r1} ==> r1c6 <> 8
biv-chain[2]: r2c5{n8 n9} - r1c4{n9 n8} ==> r2c6 <> 8
biv-chain[2]: r1c7{n8 n9} - r1c4{n9 n8} ==> r1c2 <> 8
biv-chain[2]: r1n6{c2 c6} - r1n5{c6 c2} ==> r1c2 <> 9
whip[2]: c5n9{r5 r2} - r1n9{c4 .} ==> r5c7 <> 9
biv-chain[3]: c2n7{r5 r7} - r9c3{n7 n8} - r6c3{n8 n9} ==> r5c2 <> 9
biv-chain[3]: r6c3{n8 n9} - r4c2{n9 n5} - c3n5{r4 r3} ==> r3c3 <> 8
whip[1]: b1n8{r2c1 .} ==> r8c1 <> 8
whip[3]: b4n6{r4c3 r5c3} - r5c8{n6 n9} - r6n9{c7 .} ==> r4c3 <> 9
whip[3]: b5n9{r5c4 r4c4} - r1n9{c4 c7} - b6n9{r6c7 .} ==> r5c3 <> 9
whip[3]: c3n9{r6 r3} - c3n5{r3 r4} - r4c2{n5 .} ==> r6c2 <> 9
whip[4]: r1n8{c7 c4} - b8n8{r8c4 r9c6} - c3n8{r9 r6} - r6n9{c3 .} ==> r1c7 <> 9
singles to the end