The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |53.|.9.|6.2|
 |..8|...|..1|
 |1..|..3|.5.|
 |---+---+---|
 |..7|8.9|...|
 |2..|.5.|..9|
 |...|2.7|4..|
 |---+---+---|
 |.2.|5..|..8|
 |9..|...|1..|
 |4.1|.7.|.63|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 5     3     4      |e17    9    d18     | 6     78    2      |
| 67    679   8      | 467   2     5      | 3     49    1      |
| 1     679   2      | 467  c468   3      | 789   5     47     |
|--------------------+--------------------+--------------------|
| 36    145   7      | 8     1346  9      | 2     13    56     |
| 2     14    36     |f146-3 5     146    | 78    78    9      |
| 8     15    9      | 2     136   7      | 4     13    56     |
|--------------------+--------------------+--------------------|
| 367   2     36     | 5     146   146    | 79    49    8      |
| 9     67    5      |a346  b3468  468    | 1     2     47     |
| 4     8     1      | 9     7     2      | 5     6     3      |
*--------------------------------------------------------------*

(3) r8c4 = (3-8) r8c5 = r3c5 - (8=1) r1c6 - r1c4 = (1) r5c4 => - 3 r5c4; stte

Leren

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 5     3     4     | b17    9    b18    | 6     78    2     |
 | 67    679   8     | b467   2     5     | 3     49    1     |
 | 1     679   2     | b467   468   3     | 789   5     47    |
 *-------------------+--------------------+-------------------|
 | 36    145   7     |  8     1346  9     | 2     13    56    |
 | 2     14    36    |  1346  5     146   | 78    78    9     |
 | 8     15    9     |  2     136   7     | 4     13    56    |
 *-------------------+--------------------+-------------------|
 | 367   2     36    |  5     146   146   | 79    49    8     |
 | 9     67    5     |  3-46 a3468 a468   | 1     2     47    |
 | 4     8     1     |  9     7     2     | 5     6     3     |
 *------------------------------------------------------------*


(46=8)r8c56 - (8=46)r123c4,r1c6 => -46 r8c4

[gurth]

[eleven]

(46=8)r8c56 - (8=46)r123c4,r1c6 => -46 r8c4

Nice example, how confusing this notation can be.
I see (46=8)r8c56, look at the grid, see, that if the the 2 cells don't have 46, then 3 must be in r8c5 and 8 in r8c6, so it looks correct.
Then i see that the 8's are conjugate in the 2 cells, so there must be an 8 there and the left side is false. Therefore r8c5=3 and r8c6=8

In fact, if r8c56 is not 46 or 64, it still can be 34, 36, 38, 48, 68, 84 or 86.

[gurth]

(46=8)r8c56 - (8=46)r123c4,r1c6 => -46 r8c4

Nice example, how confusing this notation can be.
I see (46=8)r8c56, look at the grid, see, that if the the 2 cells don't have 46, then 3 must be in r8c5 and 8 in r8c6, so it looks correct.
Then i see that the 8's are conjugate in the 2 cells, so there must be an 8 there and the left side is false. Therefore r8c5=3 and r8c6=8

In fact, if r8c56 is not 46 or 64, it still can be 34, 36, 38, 48, 68, 84 or 86.

Thanks for pointing this out, eleven - vastly instructive, (your discovery perhaps thanks to the fortuitous and undeniable presence of the conjugate 8s, but equally valid without them being conjugate), I'm making a special note of this case for future reference.

[SteveG48]

(46=8)r8c56 - (8=46)r123c4,r1c6 => -46 r8c4

Nice example, how confusing this notation can be.
I see (46=8)r8c56, look at the grid, see, that if the the 2 cells don't have 46, then 3 must be in r8c5 and 8 in r8c6, so it looks correct.
Then i see that the 8's are conjugate in the 2 cells, so there must be an 8 there and the left side is false. Therefore r8c5=3 and r8c6=8

In fact, if r8c56 is not 46 or 64, it still can be 34, 36, 38, 48, 68, 84 or 86.

Yes to all, including that fact that it's a bit confusing, with a need to recognize the role of the 8's. I initially thought to write it:

(3)r8c4 = (3-8)r8c5 = r8c6 - (8=1)r1c6 - (1=3)r1238c4 => -46 r8c4,

which is easier to follow. I chose to write it the way I did because it rather tickled my funny bone, and I thought others might find it interesting.

[ArkieTech]

How about?

Code: Select all

 *-----------------------------------------------------------*
 | 5     3     4     |a17    9    a18    | 6     78    2     |
 | 67    679   8     |a467   2     5     | 3     49    1     |
 | 1     679   2     |a467   468   3     | 789   5     47    |
 |-------------------+-------------------+-------------------|
 | 36    145   7     | 8     1346  9     | 2     13    56    |
 | 2     14    36    | 1346  5     146   | 78    78    9     |
 | 8     15    9     | 2     136   7     | 4     13    56    |
 |-------------------+-------------------+-------------------|
 | 367   2     36    | 5    b146  b146   | 79    49    8     |
 | 9     67    5     | 3-46  3468 b468   | 1     2     47    |
 | 4     8     1     | 9     7     2     | 5     6     3     |
 *-----------------------------------------------------------*
(46=718)r123c4,r1c6-(18=46)r78c6,r7c5 => -46r8c4; ste


[Leren]

Code: Select all

*-----------------------------------------------------------------------*
| 5      3      4       |b17     9     b18      | 6      78     2       |
| 67     679    8       |b467    2      5       | 3      49     1       |
| 1      679    2       |b467    468    3       | 789    5      47      |
|-----------------------+-----------------------+-----------------------|
| 36     145    7       | 8      1346   9       | 2      13     56      |
| 2      14     36      | 1346   5      146     | 78     78     9       |
| 8      15     9       | 2      136    7       | 4      13     56      |
|-----------------------+-----------------------+-----------------------|
| 367    2      36      | 5      146    146     | 79     49     8       |
| 9     a67     5       | 3-46   3468  a468     | 1      2     a47      |
| 4      8      1       | 9      7      2       | 5      6      3       |
*-----------------------------------------------------------------------*

A variation on Steve's move:

(46=8) r8c269 - (8=46) r123c4, r1c6 => - 36 r8c4

Leren

[daj95376]

[Withdrawn: my deductive ability has suffered greatly in recent years. Sorry!!!]

[SteveG48]

However, initially assuming two values not true does not allow him to conclude r8c4<>46.

Ordinarily, no. However, if neither of r8c56 is a 4 or a 6, then the conclusion that r23c4 is a 46 pair holds. On the other hand, if either of r8c56 is either a 4 or 6, then the other must be an 8, and r8c5 cannot be a 3. That leaves a 3 in r8c4, proving the result. I agree that the notation is questionable (at least!).

[JC Van Hay]

However, initially assuming two values not true does not allow him to conclude r8c4<>46.

Ordinarily, no. However, if neither of r8c56 is a 4 or a 6, then the conclusion that r23c4 is a 46 pair holds. On the other hand, if either of r8c56 is either a 4 or 6, then the other must be an 8, and r8c5 cannot be a 3. That leaves a 3 in r8c4, proving the result. I agree that the notation is questionable (at least!).

Then, It would have been less confusing to write :
[3r8c4=(3-8)r8c5=8r8c6-(8=17)r1c46-(7=46)r23c4]-(46=3)r8c4

[Leren]

daj95376 wrote: I'm not sure that I like Leren's representation, either

Perhaps I should have prefaced my move with ALS XZ Rule, X = 8 , Z = 4 or 6 (ie not ALS XZ Rule, X = 8 , Z = 4 and 6)

With these dual pincer ALS moves it should be understood that you have to consider the 2 pincers individually, not together, otherwise the move makes no sense.

Dan's move was similar to mine and has the same "problem". His first term (46=718)r123c4,r1c6 also has to consider 4 and 6 individually, not together, otherwise r2c4 and r3c4 are both 7 !

Leren

[eleven]

The problem with the wrong link is, that there is no ALS, because there are 4 candidates in 2 cells.

The ALS chains of Dan and Leren are out of question.

Personally i prefer, when such chains are written as simple as possible, without pressing simple links into one ALS link.

E.g Dan's cahin i would write as
(46=7)r23c4-(7=1)r1c4-(1=8)r1c6-(8=146)r78c6,r7c5 => -46r8c4
and Leren's as
(467=8)r8c269-(8=1)r1c6-(1=7)r1c4-(7=46)r23c4 => -46r8c4

But i see, that you like to play with that to notate shorter solutions.

@Danny: if you have an ALS, you always have a link between different sets of candidates, e.g. abc=defg for a 6 cell ALS. The question is just, if it is of use.
It seems to be convention here to leave out candidates on one side, if they are not used (so a=b also would be a valid link in the 6 cell ALS).

[daj95376]

Okay, I hope that I have my act together now.

If you rearrange SteveG48's chain to read from r-to-l, then you get [ - 8r8c6 = 46r8c56 ] for the rightmost SL. However,

- 8r8c6 = (467)r8c269 - (46)r8c5

prevents r8c5 from containing 4 or 6. Thus, the SL is inaccurate. The problem is that only part of the actual SL is presented. It should be:

(46=38)r8c56

Until the pair "38" is deleted from r8c56, you can't deduce r8c56=46.

Now, here's where I get a headache. SteveG48's chain works just fine when I treat it as part of a forcing chain:

Code: Select all

 (46   )r8c56                       - (46)r8c4
         ||
 (46=38)r8c56 - (8=1746)r1c46,r23c4 - (46)r8c4          [SteveG48]


===== ===== =====

I like:

Code: Select all

 +---------------------------------------------------------------+
 |  5     3     4     |  a17    9    b18    |  6     78    2     |
 |  67    679   8     |  a467   2     5     |  3     49    1     |
 |  1     679   2     |  a467   468   3     |  789   5     47    |
 |--------------------+---------------------+--------------------|
 |  36    145   7     |   8     1346  9     |  2     13    56    |
 |  2     14    36    |   1346  5     146   |  78    78    9     |
 |  8     15    9     |   2     136   7     |  4     13    56    |
 |--------------------+---------------------+--------------------|
 |  367   2     36    |   5     146   146   |  79    49    8     |
 |  9    c67    5     | da346   3468 c468   |  1     2    c47    |
 |  4     8     1     |   9     7     2     |  5     6     3     |
 +---------------------------------------------------------------+
 # 58 eliminations remain

 discontinuous loop  =>  r8c4=3

 (3=1467)r1238c4 - (1=8)r1c6 - (8=467)r8c269 - (46=3)r8c4


_