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[Yogi]

......51..7.3............8...7.51....2....6.3.........4..6..2..1.5.4.............

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[Leren]

Code: Select all

*------------------------------------------*
| 3  4  689 | 7   2   689 |  5   1    69   |
| 5  7  689 | 3   1   689 |ha9-4 246 b2469 |
| 2  1  69  | 5   69  4   |  3   8    7    |
|-----------+-------------+----------------|
| 6  3  7   |d289 5   1   | c489 24  c2489 |
| 89 2  1   | 4   89  7   |  6   5    3    |
| 89 5  4   | 289 36  36  |  1   7    289  |
|-----------+-------------+----------------|
| 4  8  3   | 6   7   5   |  2   9    1    |
| 1  69 5   |e89  4   2   |  7   3   f68   |
| 7  69 2   | 1   389 39  | g48  46   5    |
*------------------------------------------*

4 r2c7 - r2c9   = (4-8) r4c9   \
                               |
4 r2c7 - 9 r2c7 = (9-8) r4c7   = (8) r4c4 - r8c4 = r8c9 - (8=4) r9c7 - 4 r2c7 => - 4 r2c7; stte

Leren

[Cenoman]

Code: Select all

 +------------------+--------------------+---------------------+
 |  3    4    689   |  7     2     689   |  5     1     69     |
 |  5    7    689   |  3     1     689   |  9-4   246  B2469   |
 |  2    1    69    |  5     69    4     |  3     8     7      |
 +------------------+--------------------+---------------------+
 |  6    3    7     |  289*  5     1     |  489*  24   A2489#  |
 |  89   2    1     |  4     89*   7     |  6     5     3      |
 |  89   5    4     | a289#  36    36    |  1     7     289    |
 +------------------+--------------------+---------------------+
 |  4    8    3     |  6     7     5     |  2     9     1      |
 |  1    69   5     | b89    4     2     |  7     3    c68     |
 |  7    69   2     |  1     389*  39    | d48*   46    5      |
 +------------------+--------------------+---------------------+

5-links oddagon in the 8s (*) with two guardians (#)
(8)r6c4 - r8c4 = r8c9 - (8=4)r9c7
(8-4)r4c9 = (4)r2c9
=> -4 r2c7; ste

[pjb]

Code: Select all

 3       4       689    | 7      2      689    | 5      1      69     
 5       7       689    | 3      1      689    | 9-4    246   f2469   
 2       1       69     | 5      69     4      | 3      8      7     
------------------------+----------------------+---------------------
 6       3       7      |d289    5      1      | 489    24    e2489   
 89      2       1      | 4      89     7      | 6      5      3     
 89      5       4      | 289    36     36     | 1      7      289   
------------------------+----------------------+---------------------
 4       8       3      | 6      7      5      | 2      9      1     
 1       69      5      |c89     4      2      | 7      3     b68     
 7       69      2      | 1      389    39     |a48     46     5     


(4=8)r9c7 - (r4c7)r8c9 = r8c4 - r4c4 = (8-4)r4c9 = r2c9 => -4 r2c7; stte

Phil

[Leren]

pjb wrote : (4=8)r9c7 - (r4c7)r8c9 = r8c4 - r4c4 = (8-4)r4c9 = r2c9 => -4 r2c7; stte

Hi Phil, you need to fix an obvious typo. Leren

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 3     4     689   | 7     2     689   |  5     1     69    |
 | 5     7     689   | 3     1     689   | a9-4   246  g2469  |
 | 2     1     69    | 5     69    4     |  3     8     7     |
 *-------------------+-------------------+--------------------|
 | 6     3     7     |d289   5     1     |bc489  e24   f2489  |
 | 89    2     1     | 4     89    7     |  6     5     3     |
 | 89    5     4     | 289   36    36    |  1     7     289   |
 *-------------------+-------------------+--------------------|
 | 4     8     3     | 6     7     5     |  2     9     1     |
 | 1     69    5     |d89    4     2     |  7     3     68    |
 | 7     69    2     | 1    c389  c39    |bc48    46    5     |
 *------------------------------------------------------------*


The same as Phil and Leren, expressed a little differently:

(9=4)r2c7 - 4r49c7 = ((89)r49c7)&((389)r9c567) - (9=28)r48c4 - (2=4)r4c8 - r4c9 = 4c2c9 => -4 r2c7 ; stte

[eleven]

Code: Select all

 *-------------------------------------------------------------*
 |  3    4    689   |  7     2     689   |  5     1    b69     |
 |  5    7    689   |  3     1     689   | c49    246   2469   |
 |  2    1    69    |  5     69    4     |  3     8     7      |
 |------------------+--------------------+---------------------|
 |  6    3    7     |  2-89  5     1     | d89-4  24    2489   |
 |  89   2    1     |  4     89    7     |  6     5     3      |
 |  89   5    4     |  289   36    36    |  1     7     289    |
 |------------------+--------------------+---------------------|
 |  4    8    3     |  6     7     5     |  2     9     1      |
 |  1    69   5     |ga89    4     2     |  7     3   fb68     |
 |  7    69   2     |  1     389   39    | e48    46    5      |
 *-------------------------------------------------------------*

Remote pair 89 in r4c7,r8c4:
(9=8)r8c4 - (8=9)r18c9 - r2c7 = (9-8)r4c7 = r9c7 - r8c9 = 8r8c4, loop => -89r4c4, stte

[SteveG48]

Code: Select all

 *-------------------------------------------------------------*
 |  3    4    689   |  7     2     689   |  5     1    b69     |
 |  5    7    689   |  3     1     689   | c49    246   2469   |
 |  2    1    69    |  5     69    4     |  3     8     7      |
 |------------------+--------------------+---------------------|
 |  6    3    7     |  2-89  5     1     | d89-4  24    2489   |
 |  89   2    1     |  4     89    7     |  6     5     3      |
 |  89   5    4     |  289   36    36    |  1     7     289    |
 |------------------+--------------------+---------------------|
 |  4    8    3     |  6     7     5     |  2     9     1      |
 |  1    69   5     |ga89    4     2     |  7     3   fb68     |
 |  7    69   2     |  1     389   39    | e48    46    5      |
 *-------------------------------------------------------------*

Remote pair 89 in r4c7,r8c4:
(9=8)r8c4 - (8=9)r18c9 - r2c7 = (9-8)r4c7 = r9c7 - r8c9 = 8r8c4, loop => -89r4c4, stte

Nice! I'm not so sure that I'd call it a loop so much as a chain within a chain. In any case, the loop aspect of it also gives you -69r2c9.

[Leren]

eleven wrote : (9=8)r8c4 - (8=9)r18c9 - r2c7 = (9-8)r4c7 = r9c7 - r8c9 = 8r8c4, loop

I don't understand this. The parity of the candidates in the start cell r8c4 appear to be the wrong way round. Leren

[Leren]

Steve G48 wrote I'm not so sure that I'd call it a loop so much as a chain within a chain. In any case, the loop aspect of it also gives you -69r2c9.

I doesn't look like a loop to me at all, I've just asked eleven to have a look at it. - 69 r2c9 is correct because of the 6 cell DP (689) in r12c479, but that doesn't solve the puzzle.

Leren

[pjb]

Leren
You will have to help. I can't see the problem.
Phil

[SteveG48]

Steve G48 wrote I'm not so sure that I'd call it a loop so much as a chain within a chain. In any case, the loop aspect of it also gives you -69r2c9.

I doesn't look like a loop to me at all, I've just asked eleven to have a look at it. - 69 r2c9 is correct because of the 6 cell DP (689) in r12c479, but that doesn't solve the puzzle.

Leren

(9=8)r8c4 - (8=9)r18c9 - r2c7 = (9-8)r4c7 = r9c7 - r8c9 = 8r8c4, loop => -89r4c4, stte

Well, I agree that it's not a loop as written. However, if we rewrite it as [(9=8)r8c4 - (8=9)r18c9 - r2c7 = 9r4c7] - [8r4c7 = r9c7 - r8c9 = 8r8c4], breaking it into 2 parts, then we get Eleven's eliminations.

The loop that's contained in it is (8=6)r8c9 - (6=9)r1c9 - r2c7 = (9-8)r4c7 = r9c7 - r8c9 loop. That gives the extra eliminations that I pointed to. They don't really contribute.

[Leren]

pjb wrote : Leren. You will have to help. I can't see the problem.

OK I can see it now (4=8)r9c7 - r4c7, r8c9 = r8c4 - r4c4 = (8-4)r4c9 = r2c9 => -4 r2c7 would be clearer to me, and you should probably indicate r4c7 somehow in your PM.

Leren

[Leren]

SteveG48 wrote :However, if we rewrite it as [(9=8)r8c4 - (8=9)r18c9 - r2c7 = 9r4c7] - [8r4c7 = r9c7 - r8c9 = 8r8c4], breaking it into 2 parts, then we get Eleven's eliminations.

I must be having a bad day. I can see that shows - 89 r4c4, which maybe solves the puzzle, but it doesn't show - 4 r4c7, which is indicated on eleven's diagram.

Leren

PS Actually there is another embedded chain in there which does give - 4 r4c7.

It's (8) r8c4 = r8c9 - r9c7 = 8 r4c7 and if you combine this with [(9=8)r8c4 - (8=9)r18c9 - r2c7 = 9r4c7] you get - 4 r4c7. As written the original move is a notational nightmare, but all the eliminations are valid ... somehow.

Leren

[SteveG48]

I must be having a bad day. I can see that shows - 89 r4c4, which maybe solves the puzzle, but it doesn't show - 4 r4c7, which is indicated on eleven's diagram.

Leren

PS Actually there is another embedded chain in there which does give - 4 r4c7.

It's (8) r8c4 = r8c9 - r9c7 = 8 r4c7 and if you combine this with [(9=8)r8c4 - (8=9)r18c9 - r2c7 = 9r4c7] you get - 4 r4c7. As written the original move is a notational nightmare, but all the eliminations are valid ... somehow.

Leren

Sorry, I should have mentioned that the loop that I pointed out gives the -4 r4c7. Since Eleven had already taken it, I didn't mention it as an extra.