The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| 1 . . | . 8 . | . . 9 |
| . . 2 | . . . | 3 . . |
| . 9 . | 6 . 5 | . 1 . |
+-------+-------+-------+
| . 7 3 | . . . | 4 6 . |
| . . . | . . . | . . . |
| . . 4 | . 9 . | 7 . . |
+-------+-------+-------+
| . 5 . | . 7 . | . 4 . |
| . . . | 1 . 9 | . . . |
| 8 . . | . 6 . | . . 5 |
+-------+-------+-------+
1...8...9..2...3...9.6.5.1..73...46............4.9.7...5..7..4....1.9...8...6...5

estimated rating: 7.1
posted with permission, has a really nice solution i thought people here would appreciate

[RSW]

I'm pretty sure this isn't the nice solution you're thinking of.

Two steps.

Code: Select all

   
 +-----------------+--------------------+---------------------+
 | 1     346  567  | 2347  8    2347    | 256   *27-5   9     |
 |x4567  468  2    | 9     14   147     | 3     x578    4678  |
 | 347   9    78   | 6     234  5       | 28     1      2478  |
 +-----------------+--------------------+---------------------+
 | 9     7    3    | 5     12   128     | 4      6      128   |
 |*26-5  1268 1568 | 23478 1234 1234678 | 12589 *2389-5 1238  |
 |x256   1268 4    | 238   9    12368   | 7     x2358   1238  |
 +-----------------+--------------------+---------------------+
 | 236   5    169  | 238   7    238     | 1269   4      1236  |
 | 23467 2346 67   | 1     5    9       | 268    2378   23678 |
 | 8     123  179  | 234   6    234     | 129    2379   5     |
 +-----------------+--------------------+---------------------+


X-Wing: (5)r26c18 => -5r5c1, r15c8

Code: Select all

 +-----------------+----------------------+------------------+
 | 1    e346  567  |ad2347  8   ad2347    |*56-2 *7-2  9     |
 |fh4567 468  2    |  9    c14    147     | 3     578  4678  |
 |fh347  9   i78   |  6    b234   5       |i28    1    2478  |
 +-----------------+----------------------+------------------+
 | 9     7    3    |  5    c12    128     | 4     6    128   |
 | 26    1268 1568 |  23478 1234  1234678 | 12589 2389 1238  |
 | 256   1268 4    |  238   9     12368   | 7     2358 1238  |
 +-----------------+----------------------+------------------+
 | 236   5    169  |  238   7     238     | 1269  4    1236  |
 |g23467 2346 67   |  1     5     9       | 268   2378 23678 |
 | 8     123  179  |  234   6     234     | 129   2379 5     |
 +-----------------+----------------------+------------------+


(2)r1c46 = (2)r3c5 - (2=14)r24c5 - (4)r1c46 = (4)r1c2 - (4)r23c1 = (4-7)r8c1 = (7)r23c1 - (7=82)r3c37 => -2r1c78; stte

Hope I didn't make a mistake. I should be in bed right now, not solving puzzles.

[P.O.]

Code: Select all

after singles and intersections:

 1        346      567      2347     8        2347     256      257      9                 
 4567     468      2        9       b1+4      147      3        578     c-4678             
d3-47     9       f7+8      6        ×234     5       g+28      1       c2+478             
 9        7        3        5       a+1±2     128      4        6        128               
 256      1268     1568     23478    1234     1234678  12589    23589    1238             
 256      1268     4        238      9        12368    7        2358     1238             
 236      5        169      238      7        238      1269     4        1236             
d23+467   2346    e6*7      1        5        9        268      2378     23678             
 8        123     e1*79     234      6        234      129      2379     5                 


r4c5{n2 n1} - r2c5{n1 n4} - c9n4{r2 r3} - c1n4{r3 r8} - b7n7{r8c1 r8c3r9c3} - r3c3{n7 n8} - r3c7{n8 n2} => r3c5 <> 2
then intersections on 2 + xwing on 5
ste.

[marek stefanik]

Code: Select all

.--------------------.------------------------.---------------------.
| 1      346  *567   | 2347    8      2347    |*256    27–5   9     |
| 4567   468   2     | 479     14     147     | 3      578    4678  |
| 347    9     78    | 6       234    5       | 28     1      2478  |
:--------------------+------------------------+---------------------:
| 259    7     3     | 258     125    128     | 4      6      128   |
| 269–5  1268 *159–68| 23478–5 1234–5 1234678 |*159–28 2389–5 1238  |
| 256    1268  4     | 2358    9      12368   | 7      2358   1238  |
:--------------------+------------------------+---------------------:
| 2369   5    #169   | 238     7      238     |#12689  4      12368 |
| 23467  2346  67    | 1       2345   9       | 268    2378   23678 |
| 8      1234 #179   | 234     6      234     |#129    2379   5     |
'--------------------'------------------------'---------------------'

X-Wing 5c37\r15, in r5 we get a pair with the external of UR 19r79c37, stte

Marek

[jco]

Code: Select all

.--------------------------------------------------------------------.
| 1      346   a567   | 2347   8     2347    | e256    d257    9     |
| 4567   468    2     | 9      14    147     |  3      d578    4678  |
| 347    9      78    | 6      234   5       | d28      1      2478  |
|---------------------+----------------------+-----------------------|
| 9      7      3     | 5      12    128     |  4       6      128   |
| 256    1268   168-5 | 23478  1234  1234678 | f12589   23589  1238  |
| 256    1268   4     | 238    9     12368   |  7       2358   1238  |
|---------------------+----------------------+-----------------------|
| 236    5      169   | 238    7     238     |  1269    4      1236  |
| 23467  2346  a67    | 1      5     9       |  268     2378   23678 |
| 8      123   b179   | 234    6     234     |  129    c2379   5     |
'--------------------------------------------------------------------'

1. ALS W-wing with transport (5=67)r18c3 - r9c3 = r9c8 - (7=285)b3p257 - (5)r1c7 = (5)r5c7 => -5 r5c3 [5 placements & lcls]

Code: Select all

.------------------------------------------------------------.
| 1      346   5   | 2347   8     2347    | 26   27    9     |
| 467    468   2   | 9      14    147     | 3    5     4678  |
| 347    9     78  | 6      234   5       | 28   1     2478  |
|------------------+----------------------+------------------|
| 9      7     3   | 5      12    128     | 4    6     128   |
| 26     1268  168 | 23478  1234  1234678 | 5    9     1238  |
| 5      1268  4   | 238    9     12368   | 7    238   1238  |
|------------------+----------------------+------------------|
| 236    5    *19  | 238    7     238     |*19   4     236   |
| 23467  2346  67  | 1      5     9       | 268  2378  23678 |
| 8      123  *19+7| 234    6     234     |*19   237   5     |
'------------------------------------------------------------'

Uniqueness (19)r79c37 => +7 r9c3; ste

[Cenoman]

X-Wing 5c37\r15, in r5 we get a pair with the external of UR 19r79c37, stte

Applause !

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 1       346     567     ! 2347    8       2347    ! 256     257     9       !
   ! 4567    468     2       ! 9       14      147     ! 3       578     4678    !
   ! 347     9       78      ! 6       234     5       ! 28      1       2478    !
   +-------------------------+-------------------------+-------------------------+
   ! 9       7       3       ! 5       12      128     ! 4       6       128     !
   ! 256     1268    1568    ! 23478   1234    1234678 ! 12589   23589   1238    !
   ! 256     1268    4       ! 238     9       12368   ! 7       2358    1238    !
   +-------------------------+-------------------------+-------------------------+
   ! 236     5       169     ! 238     7       238     ! 1269    4       1236    !
   ! 23467   2346    67      ! 1       5       9       ! 268     2378    23678   !
   ! 8       123     179     ! 234     6       234     ! 129     2379    5       !
   +-------------------------+-------------------------+-------------------------+
187 candidates

1) Very elementary, simplest-first solution, with 3 non-W1 steps in W3 - my preferred solution.

x-wing-in-rows: n5{r2 r6}{c1 c8} ==> r5c8≠5, r5c1≠5, r1c8≠5
biv-chain[3]: r3c3{n7 n8} - r3c7{n8 n2} - r1c8{n2 n7} ==> r1c3≠7, r3c9≠7
whip[1]: r3n7{c3 .} ==> r2c1≠7
biv-chain[3]: b1n3{r1c2 r3c1} - c1n7{r3 r8} - b7n4{r8c1 r8c2} ==> r8c2≠3, r1c2≠4
whip[1]: r1n4{c6 .} ==> r2c5≠4, r2c6≠4, r3c5≠4
stte



2) Solution with 2 non-W1 steps in W5. Absurdly complicated considering the previous solution.

whip[5]: r3c3{n7 n8} - r3c7{n8 n2} - r1c8{n2 n5} - r2n5{c8 c1} - r6n5{c1 .} ==> r3c9≠7
whip[1]: r3n7{c3 .} ==> r1c3≠7, r2c1≠7
biv-chain[3]: b1n3{r1c2 r3c1} - c1n7{r3 r8} - b7n4{r8c1 r8c2} ==> r1c2≠4, r8c2≠3
stte

[shye]

wonderful solutions all around! marek found the authors intentions

thought i'd provide a different non-uniqueness based solution which i reckon is nice,
after the x-wing on 5s:

Code: Select all

.--------------------.----------------------.--------------------.
|  1     *346   567  |*2347   8    *2347    | 256    27    9     |
|  4567   468   2    | 9      1-4   147     | 3      578  *4678  |
|f*347    9     78   | 6      234   5       | 28     1   f*2478  |
:--------------------+----------------------+--------------------:
|  9      7     3    | 5      12    128     | 4      6     128   |
|  26     1268  1568 | 23478  1234  1234678 | 12589  2389  1238  |
|  256    1268  4    | 238    9     12368   | 7      2358  1238  |
:--------------------+----------------------+--------------------:
|  236    5     169  | 238    7     238     | 1269   4     1236  |
|f*23467 *2346  67   | 1      5     9       | 268    2378  23678 |
|  8      123   179  | 234    6     234     | 129    2379  5     |
'--------------------'----------------------'--------------------'

kraken firework
7s multi-candidate strong link is true else repeat 7s in b1
||(7-3)r3c1 = (3-4)r1c2 = 4r1c46
||(7-4)r3c9 = 4r2c9
||(7-4)r8c1 = 4r8c2 - 4r1c2 = 4r1c46
-4r2c5 stte

[denis_berthier]

Code: Select all

.--------------------.----------------------.--------------------.
|  1     *346   567  |*2347   8    *2347    | 256    27    9     |
|  4567   468   2    | 9      1-4   147     | 3      578  *4678  |
|f*347    9     78   | 6      234   5       | 28     1   f*2478  |
:--------------------+----------------------+--------------------:
|  9      7     3    | 5      12    128     | 4      6     128   |
|  26     1268  1568 | 23478  1234  1234678 | 12589  2389  1238  |
|  256    1268  4    | 238    9     12368   | 7      2358  1238  |
:--------------------+----------------------+--------------------:
|  236    5     169  | 238    7     238     | 1269   4     1236  |
|f*23467 *2346  67   | 1      5     9       | 268    2378  23678 |
|  8      123   179  | 234    6     234     | 129    2379  5     |
'--------------------'----------------------'--------------------'

kraken firework
7s multi-candidate strong link is true else repeat 7s in b1
||(7-3)r3c1 = (3-4)r1c2 = 4r1c46
||(7-4)r3c9 = 4r2c9
||(7-4)r8c1 = 4r8c2 - 4r1c2 = 4r1c46
-4r2c5 stte

You count this as 2 steps, right?
- one step for establishing the "strong-link",
- plus one step for the Kraken thing, which in my view is a Forcing{3}-S2-whip[8]

Starting with the same resolution state as you:

Code: Select all

   +-------------------------+-------------------------+-------------------------+
   ! 1       346     567     ! 2347    8       2347    ! 256     27      9       !
   ! 4567    468     2       ! 9       14      147     ! 3       578     4678    !
   ! 347     9       78      ! 6       234     5       ! 28      1       2478    !
   +-------------------------+-------------------------+-------------------------+
   ! 9       7       3       ! 5       12      128     ! 4       6       128     !
   ! 26      1268    1568    ! 23478   1234    1234678 ! 12589   2389    1238    !
   ! 256     1268    4       ! 238     9       12368   ! 7       2358    1238    !
   +-------------------------+-------------------------+-------------------------+
   ! 236     5       169     ! 238     7       238     ! 1269    4       1236    !
   ! 23467   2346    67      ! 1       5       9       ! 268     2378    23678   !
   ! 8       123     179     ! 234     6       234     ! 129     2379    5       !
   +-------------------------+-------------------------+-------------------------+

and targeting the same candidate, the solution can be found in 1 non-W1 step in W6:
whip[6]: c9n4{r2 r3} - b1n4{r3c1 r1c2} - b1n3{r1c2 r3c1} - r3n7{c1 c3} - c1n7{r2 r8} - r8n4{c1 .} ==> r2c5≠4

[shye]

You count this as 2 steps, right?
- one step for establishing the "strong-link",
- plus one step for the Kraken thing, which in my view is a Forcing{3}-S2-whip[8]

personally i see it as one step. but the whole path is two because of the x-wing from earlier

i know people have different perspectives on what counts as a step, so recently ive decided not to mention step count. its less important, sharing the logic is the fun part

[denis_berthier]

You count this as 2 steps, right?
- one step for establishing the "strong-link",
- plus one step for the Kraken thing, which in my view is a Forcing{3}-S2-whip[8]

personally i see it as one step. but the whole path is two because of the x-wing from earlier
i know people have different perspectives on what counts as a step, so recently ive decided not to mention step count. its less important, sharing the logic is the fun part

I don't really take the number of steps seriously; it's always a matter of balancing it with the length of chains or the size of other patterns.
Unfortunately, in many of the solutions proposed on this forum, the balance chosen implies absurdly complicated patterns.
It's difficult for me to see any fun in overly complicated solutions, when an elementary one exists.

[marek stefanik]

X-Wing 5c37\r15, in r5 we get a pair with the external of UR 19r79c37, stte

Applause !

Thanks Cenoman, but it's way easier to just find the solution than to come up with the idea and then design a puzzle around it.
RSP deserves all the credit.

You count this as 2 steps, right?
- one step for establishing the "strong-link",
- plus one step for the Kraken thing, which in my view is a Forcing{3}-S2-whip[8]

Hi Denis,
Can you explain the substantial difference between S-whips and Kraken Fireworks/Fish that makes you believe that the fish inside the latter should be counted as steps?

I think you got lost in the notation, there are no inner subsets in shye's pattern and the length also seems off.
The structure in the grid is almost the same as in your whip[6], it can be described like this (I'm not sure what you would call it, I think it's some kind of braid[6]):
c9n4{r2 r3} - r1n4{c4 c2} - b1n3{r1c2 r3c1} - r3n7{c1 c3} - c1n7{r2 r8} - r8n4{c1 .} ==> r2c5≠4

Marek

[denis_berthier]

You count this as 2 steps, right?
- one step for establishing the "strong-link",
- plus one step for the Kraken thing, which in my view is a Forcing{3}-S2-whip[8]

Hi Denis,
Can you explain the substantial difference between S-whips and Kraken Fireworks/Fish that makes you believe that the fish inside the latter should be counted as steps?

If there's a Fish inside a chain, it's counted in the length of the chain - not as a step.
In Shye's presentation, there is first a proof (of undefined complexity) of a "strong link" (her terms) and then this is used in the Kraken thing: 2 independent steps.

The structure in the grid is almost the same as in your whip[6], it can be described like this (I'm not sure what you would call it, I think it's some kind of braid[6]):c9n4{r2 r3} - r1n4{c4 c2} - b1n3{r1c2 r3c1} - r3n7{c1 c3} - c1n7{r2 r8} - r8n4{c1 .} ==> r2c5≠4

There's no "structure in the grid". The only structures there can be are those one writes explicitly.
Clearly, Shye's presentation is not a whip or a braid; it's a forcing-something - like any Kraken.
Whether it can be re-written in different ways is another question. I've already shown that it can be replaced by a whip[6].

[shye]

Whether it can be re-written in different ways is another question. I've already shown that it can be replaced by a whip[6].

i had a think about it now and noticed that kraken fireworks with at least one line having only one position outside the intersecting box can always be seen as regular kraken line (and subsequently added that note to my write-up about them). so for this one, im not surprised theres a simpler representation, but its the representation i first found and i thought it was interesting, so i gave it a share. the firework kraken saves on one strong link but i dont think i can argue its as simple as looking at where x can go in a line

It's difficult for me to see any fun in overly complicated solutions, when an elementary one exists.

thats fair. for me theyre fun because theyre interesting, stuff i havent thought about yet, sudoku would get a bit monotonous without that

[marek stefanik]

In Shye's presentation, there is first a proof (of undefined complexity) of a "strong link" (her terms) and then this is used in the Kraken thing: 2 independent steps.

Not Kraken 'thing', Kraken Firework. Unlike the complexity of 'thing', the complexity of fireworks is clearly defined (they're finned mutant x-wings).
Whether they are independent or not is a matter of opinion, one can even think of any link in a chain as of a step of its own if they wish so.

There's no "structure in the grid". The only structures there can be are those one writes explicitly.

The entire point of any notation is to represent the structures in the grid.
These representations can have their own structure, but they are mere descriptions.
That allows you to match equivalent patterns even if the ways they're presented are completely different, such as the kraken and the braid.
I honestly don't understand your POV on this.

the firework kraken saves on one strong link

I'm not sure it does, since you need two strong links to get the firework you build the kraken on, instead of just one for a line.
But I agree that if you were to use it multiple times, then it would be clearly better than combining the two strong links over and over.

Marek