The New Sudoku Players' Forum

[DonM]

Don, you purporting expert, Look at 479r89c8 : 7r5c8 looks like a natural target (which doesn't mean that it will turn out to be one).
The logic :
either r89c9 is the hidden pair 47, or there is a 9 in r89c9.
If it is the pair, the case is closed : <7>r5c8
If it isn't, then a little chain with 9 soon places 7 in r5c2.
For variety as compared to your steps :
9r89c8-(9=3)r2c8-(3=5)r1c9-(5=8)r1c2-(8=24)r89c2-(4=7)r5c2 : <7>r5c8
That reasoning is then combined into one chain :
47r89c8=9r89c8-(9=3)r2c8-(3=5)r1c9-(5=8)r1c2-(8=24)r89c2-(4=7)r5c2 : <7>r5c8.

Purporting a little on this:

My sense is that when it comes to sudoku as simply a puzzle game, people's brains operate in several ways ie. they see the structures and patterns in different individual ways and solve accordingly. Broadly, I think that some people start by seeing pure patterns (as in pattern A) and others clearly see the underlying logical relationships and early-on express them as chains particularly (IMO) if they have a strong math/logic background or just a God-given talent. However, I think that most start by solving in a pattern A way because fewer people have the gifts/experience to right away see the logic that leads to chains, something that seems to be inferred by the fact that most of the tutorials start by pointing out patterns such as x-wings and the like.

With that in mind, what you point out above is extremely useful because those who are early in their solving experience can see your perspective and compare it with my graphic. There may be some who immediately pick up on the logic of your approach and if so, they will make a quantum leap in their solving. The chains will always be both the most difficult to pick up on and the most powerful.

[ronk]

Relevantly, observe that by analogy to your use of the ALS xy wing term, the below is an xy-wing.

Relevant grammar : by analogy with/analogous to

The accursed shark alone can in any generic respect be said to bear comparative analogy to him. -- Melville, Herman. Moby Dick

... so I'll stand by my grammar. Slow day for you, eh?

[aran]

Mutant rank 1 to rank 0 promotion fish, r8c9<>4

I have always wanted to ask to how describe this. In terms of cover sets, the triplet 4r6c5 lowers the rank on the right to 0 to eliminate 4r8c9. I'm sure there is a better way.

I would start with this.

Code: Select all

 .  .  . |  4  .  4 |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
*4  .  . | *4  . *4 |  .  . *4
 .  4  . |  4  .  4 |  .  4  .
 .  .  . |  . *4  . |  .  . *4
---------+----------+----------
*4  .  . |  . #4  . |  .  . *4
 4  4  . |  4  .  4 |  .  4 -4
 4  4  . |  4  .  4 |  .  4  .

finned franken swordfish r467\c19b5 plus fin r7c5

r8c9 -4- r6c9 =4= r6c5 -4- fin:r7c5 =4= swordfish:r467\c19b5 -4- r8c9 ==> r8c9<>4

Either the unfinned (franken) swordfish is true or the fin cell is true.
If the unfinned swordfish is true: r467\c19b5 -4- r8c9
If the fin is true: r7c5 -4- r6c5 =4= r6c9 -4- r8c9

The r7c5 -4- r6c5 segment corresponds to 4c5 being a linkset member. Alternatively, the fish could be considered to be finned swordfish r467\c159 plus fin r4c46.

Interestingly, neither POV puts the fin at the linkset triple r6c5.

The linkset triple r6c5 works like an anti-fin :

fin :
fin false=>fish/rank 0=><z>
fin true=><z>

anti-fin :
anti-fin true=>fish/rank 0=><z>
anti-fin false=><z>

[ronk]

That reasoning is then combined into one chain :
47r89c8=9r89c8-(9=3)r2c8-(3=5)r1c9-(5=8)r1c2-(8=24)r89c2-(4=7)r5c2 : <7>r5c8.

You've got a legitimate ALS xy-wing there. A bit disguised in that notation, but an ALS xy-wing nonetheless.

r5c8 -7- als:r289c8 -3- als:r1c29 - 8- als:r589c2 -7- r5c8 ==> r5c8<>7

Nice path, but you can get by with the strong inferences of four bilocal/bivalues (six cells) instead of the strong sets of eight cells.

Code: Select all

 18   *58    9     | 34    2     134   | 7     6    *35
 27   *257   4     | 39    6     8     | 1    *39    25
 12    3     6     | 5     19    7     | 4     8     29
-------------------+-------------------+------------------
 47    1     2     | 469   379   346   | 8     5     347
 5    *47    8     | 234   137   1234  | 9     34-7  6
 6     9     3     | 8     47    5     | 2     1     47
-------------------+-------------------+------------------
 348   6     7     | 1     34    9     | 5     2     48
 23489 248   1     | 2347  5     234   | 6     479   4789
 249   24    5     | 2467  8     246   | 3     479   1

 r5c8 =3= r2c8- 3- r1c9- 5- r1c2 =5= r2c2 =7= r5c2 -7- r5c8 ==> r5c8<>7

[aran]

Relevantly, observe that by analogy to your use of the ALS xy wing term, the below is an xy-wing.

Relevant grammar : by analogy with/analogous to

The accursed shark alone can in any generic respect be said to bear comparative analogy to him. -- Melville, Herman. Moby Dick

so I'll stand by my grammar. Slow day for you, eh?

comparative analogy

If he wasn't beyond the occasional tautology, perhaps he was also prone to the occasional prepositional lapse...

[aran]

(...) because those who are early in their solving experience can see your perspective and compare it with my graphic. There may be some who immediately pick up on the logic of your approach and if so, they will make a quantum leap in their solving. The chains will always be both the most difficult to pick up on and the most powerful.

Don
That was exactly my purpose and I appreciate your post.

[aran]

Nice path, but you can get by with the strong inferences of four bilocal/bivalues (six cells) instead of the strong sets of eight cells.

Code: Select all

 18   *58    9     | 34    2     134   | 7     6    *35
 27   *257   4     | 39    6     8     | 1    *39    25
 12    3     6     | 5     19    7     | 4     8     29
-------------------+-------------------+------------------
 47    1     2     | 469   379   346   | 8     5     347
 5    *47    8     | 234   137   1234  | 9     34-7  6
 6     9     3     | 8     47    5     | 2     1     47
-------------------+-------------------+------------------
 348   6     7     | 1     34    9     | 5     2     48
 23489 248   1     | 2347  5     234   | 6     479   4789
 249   24    5     | 2467  8     246   | 3     479   1

 r5c8 =3= r2c8- 3- r1c9- 5- r1c2 =5= r2c2 =7= r5c2 -7- r5c8 ==> r5c8<>7

I can find an even longer path
Xwing 7r89c8
+long-tailed fin 7r8c9=>7r5c2 (via 6r9c6)

[Luke]

This looks "blossomy" to me, but whatever it is, it seems to work: one set in c6, one in c4, and a bivalue as a third set in between:

Code: Select all

*--------------------------------------------------------------------*
 | 18     58     9      |*34     2     *134    | 7      6      35     |
 | 27     257    4      |*39     6      8      | 1      39     25     |
 | 12     3      6      | 5     *19     7      | 4      8      29     |
 |----------------------+----------------------+----------------------|
 | 47     1      2      | 469    379   *346    | 8      5      347    |
 | 5      47     8      |*234    137   -2134   | 9      347    6      |
 | 6      9      3      | 8      47     5      | 2      1      47     |
 |----------------------+----------------------+----------------------|
 | 348    6      7      | 1      34     9      | 5      2      48     |
 | 23489  248    1      |-2347   5     *234    | 6      479    4789   |
 | 249    24     5      |-2467   8     *246    | 3      479    1      |
 *--------------------------------------------------------------------*


(2346)r1489c6=(1)r1c6-(1=9)r3c5-(9)r2c4=(234)r125c4 => r89c4 and r5c6<>2.

[aran]

Code: Select all

 
 *--------------------------------------------------------------------*
 | 18     58     9      | 34     2      134    | 7      6      35     |
 | 27     257    4      | 39     6      8      | 1      39     25     |
 | 12     3      6      | 5      19     7      | 4      8      29     |
 |----------------------+----------------------+----------------------|
 | 47     1      2      | 469    379    346    | 8      5      347    |
 | 5      47     8      | 234    137    1234   | 9      347    6      |
 | 6      9      3      | 8      47     5      | 2      1      47     |
 |----------------------+----------------------+----------------------|
 | 348    6      7      | 1      34     9      | 5      2      48     |
 | 23489  248    1      | 2347   5      234    | 6      479    4789   |
 | 249    24     5      | 2467   8      246    | 3      479    1      |
 *--------------------------------------------------------------------*


Yet another way of looking at <7>r5c8
ALS A={473} r46c9
ALS B={39} r2c4
x : simple chain establishes weak link 3r4c9-3r2c4 =>A/B singly linked
=>any z which removes a candidate from both ALSs is false
7r5c8=><7>r46c9
7r5c8 via simple chain=><9>r2c4
so <7>r5c8