The New Sudoku Players' Forum

[daj95376]

re'born: You are what they call in Las Vegas ... making your point the hard way!

wapati: Using naked/hidden singles only, what is [r9c6] if [r8c2]=2 ???
(note: you should resolve the Naked Triple in [r9] first!)

[ravel]

Code: Select all

.--------------------.------------------.--------------------.
| 58     58    13    | 13    2     4    | 67    9     67     |
| 29     4     6     | 8     79    57   | 3     15    125    |
| 13     7     1239  | 13    69    56   | 25    48    48     |
:--------------------+------------------+--------------------:
| 1567   15    17    | 2     3     9    | 8     457   4567   |
| 367    9     4     | 5     67    8    | 1     2     367    |
| 23567  235   8     | 4     1     67   | 5679  357   35679  |
:--------------------+------------------+--------------------:
| 378-12 38-12 37-12 | 9     4    #12   | 257   6     1257   |
| 1279  #12    5     | 6     8     3    | 4     17    1279   |
| 4      6    *129   | 7     5    *12   |*29    138   12389  |
'--------------------'------------------'--------------------'


I don't see how r8c2 and r9c6 are the same. However, I can see that there is a Y-wing style that at least eliminates the 1's in r7c123.

Please explain, i cant spot that.
(The 2 in r7c3 can be eliminated anyway using the 29 in r9c7)

[re'born]

Code: Select all

.--------------------.------------------.--------------------.
| 58     58    13    | 13    2     4    | 67    9     67     |
| 29     4     6     | 8     79    57   | 3     15    125    |
| 13     7     1239  | 13    69    56   | 25    48    48     |
:--------------------+------------------+--------------------:
| 1567   15    17    | 2     3     9    | 8     457   4567   |
| 367    9     4     | 5     67    8    | 1     2     367    |
| 23567  235   8     | 4     1     67   | 5679  357   35679  |
:--------------------+------------------+--------------------:
| 378-12 38-12 37-12 | 9     4    #12   | 257   6     1257   |
| 1279  #12    5     | 6     8     3    | 4     17    1279   |
| 4      6    *129   | 7     5    *12   |*29    138   12389  |
'--------------------'------------------'--------------------'


I don't see how r8c2 and r9c6 are the same. However, I can see that there is a Y-wing style that at least eliminates the 1's in r7c123.

Please explain, i cant spot that.
(The 2 in r7c3 can be eliminated anyway using the 29 in r9c7)

I can't spot it either. That's because it's the 2's that should be eliminated in r7c123. The links are on the 1's but the that means you eliminate the 2's. Oops. Thanks ravel. Oh and for any of this to make sense you should apply wapati's skyscraper first, and then the resulting naked triple in row 9.

[re'born]

Set r8c2 as 1, r9c6 must be one.
Set r9c6 as 2, r8c2 must be two.

Another point perhaps worth noting in this vein is the following: The first statement is logicially equivalent to the statement:
(*) r9c6<>1 => r8c2<>1
But r8c2 and r9c6 are both bivalue cells with values 1,2. So statment (*) is logically equivalent to
r9c6=2 => r8c2=2
which is second of your two statements. So, in fact, both of your assertions are equivalent, i.e., the list is redundant. Now it should be abundantly clear that the statement
r8c2=1 => r9c6=1
does not imly that
r8c2=2 => r9c6=2.

[re'born]

If you look at the pattern above that I called a "naked pair covering an xyz-wing", it imay not be readily apparent how to apply it to wapati's situation. However, if you shuffle the diagram around a bit, you will get the following version of that pattern:

Code: Select all

 .  wx .  | .  .  .  | xz  *  .
 .  .  .  | .  .  .  |  . xyz .
 .  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  .  .  | .  .  .  |  .  .  .
 .  .  .  | .  .  .  |  .  xy .
 .  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  .  .  | .  .  .  |  .  .  .
 .  *  .  | .  .  .  |  .  wx .
 .  .  .  | .  .  .  |  .  .  .


Here, we must get the same deductions as before, namely w can be removed from any *'d cell. Moreover, if w=z, then we may also remove x from any *'d cell. For wapati's situation, we take w=z=7, x=3, y=5.

There are similar patterns any time you have an xyz-wing that with its wings extended by two bivalued cells with the same candidates, one of which is the xyz-wing elimination candidate. For instance, an xyz-wing (in the form of a naked triple in a box) extended along both wings eliminates w from the *'d cell.

Code: Select all

 .  .  .  | .  .  .  | xz  .  .
 . wx  .  | .  .  .  | xy xyz .
 .  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  .  .  | .  .  .  |  .  .  .
 .  *  .  | .  .  .  | wx  .  .
 .  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  .  .  | .  .  .  |  .  .  .
 .  .  .  | .  .  .  |  .  .  .
 .  .  .  | .  .  .  |  .  .  .


[wapati]

I messed up, as you have pointed out.

The "case" I cited is valid in that the pair in r4c9 and r1c8 are cloned.
I would like to know if this "good" example can be made a pattern.
(Or a chain?)

Code: Select all

.------------------.------------------.------------------.
| 4    #37    9    | 1     8     5    | 2    *37    6    |
| 8     3567  367  | 346   346   2    | 9     1    *357  |
| 2     356   1    | 9     7     36   | 8     4    *35   |
:------------------+------------------+------------------:
| 5     6-37  2    | 8     346   3467 | 1     9    #37   |
| 1     4     367  | 3567  356   9    | 36    2     8    |
| 9     8     367  | 367   2     1    | 5     367   4    |
:------------------+------------------+------------------:
| 67    1     5    | 3467  9     8    | 346   36    2    |
| 67    2     48   | 34567 1     3467 | 346   58    9    |
| 3     9     48   | 2     456   46   | 7     58    1    |
'------------------'------------------'------------------'

My example worked, but was based on luck, not valid.
Here r9c6 and r8c2 are not actually cloned, they could have been unrelated.
Sorry!

Code: Select all

.--------------------.------------------.--------------------.
| 58     58    13    | 13    2     4    | 67    9     67     |
| 29     4     6     | 8     79    57   | 3     15    125    |
| 13     7     1239  | 13    69    56   | 25    48    48     |
:--------------------+------------------+--------------------:
| 1567   15    17    | 2     3     9    | 8     457   4567   |
| 367    9     4     | 5     67    8    | 1     2     367    |
| 23567  235   8     | 4     1     67   | 5679  357   35679  |
:--------------------+------------------+--------------------:
| 378-12 38-12 37-12 | 9     4    #12   | 257   6     1257   |
| 1279  #12    5     | 6     8     3    | 4     17    1279   |
| 4      6    *129   | 7     5    *12   |*29    138   12389  |
'--------------------'------------------'--------------------'