The New Sudoku Players' Forum

[Luke]

For those who are interested, here's a regular x-wing in an elegant little chain (different puzzle.) It was so "textbook" that I saved it in my notes. The author? Take a guess.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 2345    23459   6       | 1       238     2359    | 7       4589    234589  |
 | 2345    1      *348     |*258     7       2359    |*2358    6       234589  |
 | 7       2359   *38      | 4       238     6       |*2358    589     1       |
 |-------------------------+-------------------------+-------------------------|
 | 1348    347     2       | 6       5       347     | 9       1478    3478    |
 | 1345    6       1347    | 9       34      8       | 135     2       3457    |
 | 3458    3457    9       | 27      1       2347    | 6       4578    34578   |
 |-------------------------+-------------------------+-------------------------|
 | 9       247     47      | 3     -824      1       |*258     578     6       |
 | 6       8       147     | 257     9       2457    | 12      3       27      |
 | 123     237     5       |*278     6       27      | 4       1789    2789    |
 *-----------------------------------------------------------------------------*
 (8)r7c7=(X-wing 8's)r23c37-(8)r2c4=(8)r9c4 => r7c5<>8

From Eureka/Puzzles From Others/Vanhegan Extreme/3-19-09/ttt.

[ronk]

Code: Select all

03: Present as Dual Kraken: => r2c7<>48, some singles
 
(3)r9c2-(3)r8c1=(3)r1c1-(3=9)r1c3-(9=np48)r1c78
 ||
(9)r9c2-(9)r23c2=(9)r1c13-(9=np48)r1c78
 ||
(8)r9c2---(8=4)r7c2-(4)r4c2
       |             || 
        ------------(8)r4c2
                     ||
                    (9)r4c2-(9)r23c2=(9)r1c13-(9=np48)r1c78
                     ||
                    (7)r4c2-(7)r5c2=(7-2)r5c8=(2-1)r3c8=(1)r2c7

Similar to having three extra candidates in an AUR, at least one of any three digits of an AALS must be true.

Code: Select all

03: Present as AALS(34789)r479c2 ==> r2c7<>48

(3)r9c2-(3)r8c1=(3)r1c1-(3=9)r1c3-(9=np48)r1c78
 ||
(9)r49c2-(9)r23c2=(9)r1c13-(9=np48)r1c78
 ||
(7)r4c2-(7)r5c2=(7-2)r5c8=(2-1)r3c8=(1)r2c7

It's exactly your logic expressed a little differently. I know this is not new to you, because I've seen you post such AALS deductions before. Now if I could just find one of these things on my own.

[wintder]

For those who are interested, here's a regular x-wing in an elegant little chain (different puzzle.) It was so "textbook" that I saved it in my notes. The author? Take a guess.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 2345    23459   6       | 1       238     2359    | 7       4589    234589  |
 | 2345    1      *348     |*258     7       2359    |*2358    6       234589  |
 | 7       2359   *38      | 4       238     6       |*2358    589     1       |
 |-------------------------+-------------------------+-------------------------|
 | 1348    347     2       | 6       5       347     | 9       1478    3478    |
 | 1345    6       1347    | 9       34      8       | 135     2       3457    |
 | 3458    3457    9       | 27      1       2347    | 6       4578    34578   |
 |-------------------------+-------------------------+-------------------------|
 | 9       247     47      | 3     -824      1       |*258     578     6       |
 | 6       8       147     | 257     9       2457    | 12      3       27      |
 | 123     237     5       |*278     6       27      | 4       1789    2789    |
 *-----------------------------------------------------------------------------*
 (8)r7c7=(X-wing 8's)r23c37-(8)r2c4=(8)r9c4 => r7c5<>8

From Eureka/Puzzles From Others/Vanhegan Extreme/3-19-09/ttt.

It is a sashimi swordfish and two eliminations were missed.

Code: Select all

*-----------------------------------------------------------------------------*
 | 2345    23459   6       | 1       238     2359    | 7       4589    234589  |
 | 2345    1      *348     |*258     7       2359    |*2358    6       234589  |
 | 7       2359   *38      | 4       238     6       |*2358    589     1       |
 |-------------------------+-------------------------+-------------------------|
 | 1348    347     2       | 6       5       347     | 9       1478    3478    |
 | 1345    6       1347    | 9       34      8       | 135     2       3457    |
 | 3458    3457    9       | 27      1       2347    | 6       4578    34578   |
 |-------------------------+-------------------------+-------------------------|
 | 9       247     47      | 3       24-8    1       |*258     578     6       |
 | 6       8       147     | 257     9       2457    | 12      3       27      |
 | 123     237     5       |*278     6       27      | 4       179-8   279-8   |
 *-----------------------------------------------------------------------------*

[storm_norm]

DonM said:

Okay, so I want to know what you two guys had for breakfast.

us mortals need to eat.
pretty bold of you to assume those "two guys" would stoop to that level.
IMO.

[ttt]

Code: Select all

 *--------------------------------------------------------------------*
 | 369    1      39     | 4689   2      7      | 48     489    5      |
 | 5      269    7      | 14689  169    14689  | 148    3      2489   |
 | 4      29     8      | 5      3      19     | 6      129    7      |
 |----------------------+----------------------+----------------------|
 | 89     48(79) 2      | 3      1579   1459   | 1458   14578  6      |
 | 69     34679  459    | 1469   8      14569  | 1345   12457  234    |
 | 1      34678  345    | 46     567    2      | 9      4578   348    |
 |----------------------+----------------------+----------------------|
 | 7      48(9)  6      | 89     59     3      | 2      4589   1      |
 | 389    5      1349   | 2      169    1689   | 7      489    3489   |
 | 2      8(39)  139    | 7      4      1589   | 358    6      389    |
 *--------------------------------------------------------------------*

Similar to having three extra candidates in an AUR, at least one of any three digits of an AALS must be true.

Code: Select all

03: Present as AALS(34789)r479c2 ==> r2c7<>48

(3)r9c2-(3)r8c1=(3)r1c1-(3=9)r1c3-(9=np48)r1c78
 ||
(9)r49c2-(9)r23c2=(9)r1c13-(9=np48)r1c78
 ||
(7)r4c2-(7)r5c2=(7-2)r5c8=(2-1)r3c8=(1)r2c7

Wow..., very nice find! I didn't see it, based on your deduction then first move on my proof is not necessary.
I’ll consider this form more often later

ttt

[Luke]

It is a sashimi swordfish and two eliminations were missed.

Also missed: my point. The example was meant to show a stepping stone to the technique under discussion, which was the use of finned fish in chain propagation. Understanding one helped me understand the other. Maybe it would help someone else as well.

BTW, the gentleman I cited went on to solve that puzzle in five more moves. I'm sure you could do better if you parlay that sashimi swordfish .

[Steve K]

just for kicks and giggles, a partial hidden set version very similar to, and often complimentary with, RonK's very nice step (still uses one ALS at r1c13):

(hp29)r2c9,r3c8=(9)r1c8-(9)r1c13=[(3)r1c3 & (6)r1c1]-(36)c13Box4=(hp36)r56c2-(7)r5c2=(7-2)r2c8=(2)r3c8 => r3c8<>1

[ttt]

Code: Select all

 *--------------------------------------------------------------------*
 | 369    1      39     | 4689   2      7      | 48     489    5      |
 | 5      2(6)9  7      | 14689  169    14689  | 148    3      2489   |
 | 4      29     8      | 5      3      19     | 6      129    7      |
 |----------------------+----------------------+----------------------|
 | 89     4789   2      | 3      1579   1459   | 1458   14578  6      |
 | 69    (36)479 459    | 1469   8      14569  | 1345   12457  234    |
 | 1     (36)478 345    | 46     567    2      | 9      4578   348    |
 |----------------------+----------------------+----------------------|
 | 7      489    6      | 89     59     3      | 2      4589   1      |
 | 389    5      1349   | 2      169    1689   | 7      489    3489   |
 | 2     (3)89   139    | 7      4      1589   | 358    6      389    |
 *--------------------------------------------------------------------*

Another view for eliminating r2c7=48

Code: Select all

AAHS(36)r2569c2  => r2c7<>48
 ||
(36)r56c2-(7)r5c2=(7-2)r5c8=(2-1)r3c8=(1)r2c7
 ||
(3)r2c9-(3)r8c1=(3)r1c1-(3=9)r1c3-(9=np48)r1c78
 ||
(6)r2c2-(6)r1c1=(6-48)r1c4=(hp48)r2c46

ttt

[Allan Barker]

The following is an almost continuous nice loop, which would be a CNL except for the extra candidate 6r6c2. However, 6r6c2 loops back to 6r2c2 making a strong corner in the CNL, allowing it to eliminate 6 candidates.

As rcnb sets, it has 7 base and 7 cover sets making it rank 0 on the CNL side of the strong corner.

7 Sets = {2R2 7R5 3C12 6C2 2B6 6B1}
7 Links = {2c9 1n1 256n2 5n8 3b7} => r5c8<>145, r5c2<>49, r2c2<>9

Code: Select all

+-----------------------+--------------------+------------------------+
| 9(36)  1         39   | 4689   2     7     | 48    489       5      |
| 5      -9(26)    7    | 14689  169   14689 | 148   3         489(2) |
| 4      29        8    | 5      3     19    | 6     129       7      |
+-----------------------+--------------------+------------------------+
| 89     4789      2    | 3      1579  1459  | 1458  14578     6      |
| 69     -49(367)  459  | 1469   8     14569 | 1345  -145(27)  34(2)  |
| 1      478(36)   345  | 46     567   2     | 9     4578      348    |
+-----------------------+--------------------+------------------------+
| 7      489       6    | 89     59    3     | 2     4589      1      |
| 89(3)  5         1349 | 2      169   1689  | 7     489       3489   |
| 2      89(3)     139  | 7      4     1589  | 358   6         389    |
+-----------------------+--------------------+------------------------+

                           
(3)r8c1============(3-6)r1c1
     |                   ||
(3)r9c2=(3-6)r65c2=(6-2)r2c2=r2c9=r5c9=(2-7)r5c8=(7-6)r5c2

               |<--- Almost Continuous Nice Loop ------>|

 => r5c8<>145, r5c2<>49, r2c2<>9
 

[999_Springs]

Sigh. This is the result of a little more than one hour's work:

r9c3-3-r1c3-9-r1c78-naked pair 48-r2c7-1-r3c8=1=r3c6-1-r9c6=1=r9c3 => r9c3<>3
r5c1(-3-r8c1)-3-r1c1=3=r1c3-3-r89c3=3=r9c2-3-r9c7=3=r5c7-3-r5c1 => r5c1<>3
r8c56(-9-r7c5-5-r9c6=5=r9c7=3=r5c7=1=r4c78-1-r4c5)-9-r7c4(-8-r8c6)(-8-r12c4=8=r2c6=4=r45c6-4-r6c4-6-r12c4)-8-r9c6-naked pair r39c6-19-r8c6-6-r2c6=6=r2c5=1=r8c5-1-r9c6-9-r8c56 => r8c56<>9
r4c5-1-r8c5(-6-r2c5)=1=r89c6-1-r3c6-9-r2c5-1-r4c5 => r4c5<>1

i.e. nothing much.

I guess that getting up at midday and having breakfast at 12:20 isn't really good for sudoku solving, regardless of what I have for breakfast.

(I'm still not really sure how to write subsets in chains.)

[ronk]

r9c3-3-r1c3-9-r1c78-naked pair 48-r2c7-1-r3c8=1=r3c6-1-r9c6=1=r9c3 => r9c3<>3
...
(I'm still not really sure how to write subsets in chains.)

Nice loops are meant to read both left-to-right (L2R) and right-to-left (R2L), so I'd recommend using the ALS term. Two obvious choices for the above ...

Code: Select all

r9c3-3-r1c3-9-als:[r1c78,r2c7]-1-r3c8=1=r3c6-1-r9c6=1=r9c3

r9c3-3-r1c3-9-als:r1c78-48-aals:r2c7-1-r3c8=1=r3c6-1-r9c6=1=r9c3

When reading the latter L2R, <48> is a hidden pair which removes two candidates from the AALS. When reading R2L, <48> are two remaining candidates in the AALS, either one of which being true causes <9> to be true in the ALS.

I was going to comment on the "naked pair" in your 3rd step too, but became totally lost.