The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.2.|...|35.|
 |.57|..2|9..|
 |.49|.6.|...|
 |---+---+---|
 |..6|7.9|...|
 |..4|...|2..|
 |...|1.8|6..|
 |---+---+---|
 |...|.9.|57.|
 |..2|5..|16.|
 |.35|...|.4.|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 168     2       18     | 9      178    147    | 3      5      46     
 1368    5       7      | 348   a138    2      | 9      18     46     
 138     4       9      | 38     6      5      | 7      2      18     
------------------------+----------------------+---------------------
 5       18      6      | 7      2      9      | 4      3      18     
 89      189     4      | 36     5      36     | 2      18     7     
 2       7       3      | 1      4      8      | 6      9      5     
------------------------+----------------------+---------------------
 148     6       18     |c2348   9      134    | 5      7     d23     
 4789    89      2      | 5     b78-3   347    | 1      6     e39     
 179     3       5      | 26     17     167    | 8      4      29     


(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9 => -3 r8c5; stte

Phil

PS For those who like me dabble with patterns (POM method), no pattern of 8 includes r1c5, r235c1, r8c2, so eliminating 8 from these solves puzzle.

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 168   2     18     | 9     178   147    | 3     5     46     |
| 1368  5     7      | 348   138   2      | 9     18    46     |
| 138   4     9      | 38    6     5      | 7     2     18     |
|--------------------+--------------------+--------------------|
| 5     18    6      | 7     2     9      | 4     3     18     |
| 89    189   4      | 36    5     36     | 2     18    7      |
| 2     7     3      | 1     4     8      | 6     9     5      |
|--------------------+--------------------+--------------------|
| 148   6     18     |c2348  9     134    | 5     7    b23     |
| 4789  89    2      | 5    d78-3  347    | 1     6    a39     |
| 179   3     5      | 26    17    167    | 8     4     29     |
*--------------------------------------------------------------*

L3 Wing: (3) r8c9 = (3-2) r7c9 = (2-8) r7c4 = (8) r8c5 => - 3 r8c5; stte

Leren

[Leren]

pjb wrote : PS For those who like me dabble with patterns (POM method), no pattern of 8 includes r1c5, r235c1, r8c2, so eliminating 8 from these solves puzzle.

This suggested that a fish in 8's might do the job. Here is one.

Code: Select all

*---------------------------------------------------------------*
| *168   2    *18     | 9     178   147    | 3     5     46     |
| *1368  5     7      | 348   138   2      | 9     18    46     |
|f*138   4     9      |*38    6     5      | 7     2    *18     |
|---------------------+--------------------+--------------------|
|  5    f18    6      | 7     2     9      | 4     3    *18     |
|  9-8   189   4      | 36    5     36     | 2     18    7      |
|  2     7     3      | 1     4     8      | 6     9     5      |
|---------------------+--------------------+--------------------|
| *148   6    *18     |*2348  9     134    | 5     7     23     |
|  4789  89    2      | 5     378   347    | 1     6     39     |
|  179   3     5      | 26    17    167    | 8     4     29     |
*---------------------------------------------------------------*

Finned Franken Jellyfish in 8's r347b1 c1349 with a fin Cell r4c2 + endofin Cell r3c1 => - 8 r5c1; stte

Leren

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 168   2     18    |  9     178   147   | 3     5     46    |
 | 1368  5     7     |  348   138   2     | 9     18    46    |
 | 138   4     9     |  8-3   6     5     | 7     2     18    |
 *-------------------+--------------------+-------------------|
 | 5     18    6     |  7     2     9     | 4     3     18    |
 | 89    189   4     | C36c   5    B36    | 2     18    7     |
 | 2     7     3     |  1     4     8     | 6     9     5     |
 *-------------------+--------------------+-------------------|
 | 148   6     18    | a2348  9    A134   | 5     7     23a   |
 | 4789  89    2     |  5     378   347   | 1     6     39    |
 | 179   3     5     |  26c   17    167   | 8     4     29b   |
 *------------------------------------------------------------*

Kraken row 7 on 3's => -3 r3c4 ; stte

3r7c4                          - 3r3c4
  ||
3r7c6 - r5c6 = r5c4            - 3r3c3
  ||
(3-2)r7c9 = r9c9 - (2=63)r59c4 - 3r3c3



[Marty R.]

Deleted

[bat999]

Code: Select all

.------------------.------------------.-------------.
|  168    2     18 |  9      178  147 | 3  5    46  |
|  1368   5     7  |  348    138  2   | 9  18   46  |
|  138    4     9  |  38     6    5   | 7  2    18  |
:------------------+------------------+-------------:
|  5      18    6  |  7      2    9   | 4  3    18  |
|  89     189   4  |  36     5    36  | 2  18   7   |
|  2      7     3  |  1      4    8   | 6  9    5   |
:------------------+------------------+-------------:
|  148    6     18 | c2348   9    134 | 5  7   d23  |
|  4789  a89    2  |  5     b378  347 | 1  6    3-9 |
|  17-9   3     5  |  26     17   167 | 8  4   e29  |
'------------------'------------------'-------------'

(9=8)r8c2 - r8c5 = (8-2)r7c4 = r7c9 - (2=9)r9c9 => -9 r8c9,r9c1; stte

[bat999]

Code: Select all

 168     2       18     | 9      178    147    | 3      5      46     
 1368    5       7      | 348   a138    2      | 9      18     46     
 138     4       9      | 38     6      5      | 7      2      18     
------------------------+----------------------+---------------------
 5       18      6      | 7      2      9      | 4      3      18     
 89      189     4      | 36     5      36     | 2      18     7     
 2       7       3      | 1      4      8      | 6      9      5     
------------------------+----------------------+---------------------
 148     6       18     |c2348   9      134    | 5      7     d23     
 4789    89      2      | 5     b78-3   347    | 1      6     e39     
 179     3       5      | 26     17     167    | 8      4      29     


(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9 => -3 r8c5; stte

I have difficulty understanding some solutions.

(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9 => -3 r8c5; stte

Take it in steps.

(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9
Not 3 in r2c5 forces 3 into r8c5 and kills the 8.

(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9
Not 8 in r8c5 forces 8 into r7c4 and kills the 2.

(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9
Not 2 in r7c4 forces 2 into r7c9 and kills the 3.

(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = r8c9
Not 3 in r7c9 forces 3 into r8c9.

But stop here and look.
r8c5 contains 3 and r8c9 contains 3.
That's two threes on row 8.

Shouldn't we hear alarm bells ringing?

Doesn't it mean the solution is...
"If r2c5<>3 then we have broken the rules, we need to leave the 3 in r2c5".

I agree that r8c5<>3 (also r2c1,r2c4,r3c4<>3) because of the contradiction (r2c5 must be 3), not for any other reason.
(3)r2c5 = (3-8)r8c5 = (8-2)r7c4 = (2-3)r7c9 = (3)r8c9 => -18 r2c5; stte

Do other people see it differently?

[Marty R.]

Do other people see it differently?

I don't have a clue, but I find the subject fascinating and I hope some of the theorists weight in.

[SteveG48]

Bat, this is a hard point to get past, at times. What you need to remember is that the chain is not assigning values. It's describing relationships (links, strong and weak) between the candidates. You then use the chain to see what would happen if values were assigned. In this case, Phil notes that if r2c5 is not a 3, then r8c9 must be a 3, so 3 is eliminated in r8c5 since one or the other of r2c5 or r8c9 must be a 3 (a pincer attack).

Now note that if r8c5 is not a 3 (which we now know to be true) then r2c5 must be a 3, contradicting any assumption that it isn't. What you have noted is that if r2c5 is not a 3 then both r8c5 and r8c9 must be 3, which is a contradiction. Therefore, r2c5 must be a 3. But that is exactly equivalent to Phil's conclusion that r8c5 is not a 3. So you and Phil are both right; you've just expressed the answer differently.

[SteveG48]

All of which brings to mind this variant on Phil's solution:

Code: Select all

 *------------------------------------------------------------*
 | 168   2     18    |  9     178   147   | 3     5     46    |
 | 1368  5     7     |  348   138   2     | 9     18    46    |
 | 138   4     9     |  38    6     5     | 7     2     18    |
 *-------------------+--------------------+-------------------|
 | 5     18    6     |  7     2     9     | 4     3     18    |
 | 89    189   4     |  36    5     36    | 2     18    7     |
 | 2     7     3     |  1     4     8     | 6     9     5     |
 *-------------------+--------------------+-------------------|
 | 148   6     18    |ac2348  9    a134   | 5     7    b23    |
 | 4789  89    2     |  5    d78-3  347   | 1     6     39    |
 | 179   3     5     |  26    17    167   | 8     4     29    |
 *------------------------------------------------------------*


3r7c46 = (3-2)r7c9 = (2-8)r7c4 = 8r8c5 => -3 r8c5 ; stte

[Ngisa]

Code: Select all

+-------------+--------------+---------+
| 168  2   18 | 9    178 147 | 3 5  46 |
| 1368 5   7  | 348  138 2   | 9 18 46 |
| ad138  4   9  | e38   6   5   | 7 2  d1*8 |
+-------------+--------------+---------+
| 5    18  6  | 7    2   9   | 4 3  c18 |
| a8*9   18-9 4  | 36   5   36  | 2 b18 7  |
| 2    7   3  | 1    4   8   | 6 9  5  |
+-------------+--------------+---------+
| 148  6   18 | f2348 9   134 | 5 7  23 |
| 478-9 h89  2  | 5    g378 347 | 1 6  39 |
| 17-9  3   5  | 26   17  167 | 8 4  29 |
+-------------+--------------+---------+


(9=8*)r5c1-r5c8=r4c9-(8=1*)r3c9-(1*8*=3)r3c1-(3=8)r3c4-r7c4=r8c5-(8=9)r8c2 => -9r89c1, r5c2; stte

Clement

[Marty R.]

Bat, this is a hard point to get past, at times. What you need to remember is that the chain is not assigning values. It's describing relationships (links, strong and weak) between the candidates. You then use the chain to see what would happen if values were assigned. In this case, Phil notes that if r2c5 is not a 3, then r8c9 must be a 3, so 3 is eliminated in r8c5 since one or the other of r2c5 or r8c9 must be a 3 (a pincer attack).

Now note that if r8c5 is not a 3 (which we now know to be true) then r2c5 must be a 3, contradicting any assumption that it isn't. What you have noted is that if r2c5 is not a 3 then both r8c5 and r8c9 must be 3, which is a contradiction. Therefore, r2c5 must be a 3. But that is exactly equivalent to Phil's conclusion that r8c5 is not a 3. So you and Phil are both right; you've just expressed the answer differently.

Steve,

What's your bottom line? Is post-solution analysis a waste of time or does it have value? Do we just post our solution as long as we have a valid chain? I've been called out based on such analysis and I think I've also done some calling out.

Marty

[SteveG48]

Bat, this is a hard point to get past, at times. What you need to remember is that the chain is not assigning values. It's describing relationships (links, strong and weak) between the candidates. You then use the chain to see what would happen if values were assigned. In this case, Phil notes that if r2c5 is not a 3, then r8c9 must be a 3, so 3 is eliminated in r8c5 since one or the other of r2c5 or r8c9 must be a 3 (a pincer attack).

Now note that if r8c5 is not a 3 (which we now know to be true) then r2c5 must be a 3, contradicting any assumption that it isn't. What you have noted is that if r2c5 is not a 3 then both r8c5 and r8c9 must be 3, which is a contradiction. Therefore, r2c5 must be a 3. But that is exactly equivalent to Phil's conclusion that r8c5 is not a 3. So you and Phil are both right; you've just expressed the answer differently.

Steve,

What's your bottom line? Is post-solution analysis a waste of time or does it have value? Do we just post our solution as long as we have a valid chain? I've been called out based on such analysis and I think I've also done some calling out.

Marty

Marty, in my opinion post solution analysis is always of value. It's what you make of the analysis that determines whether you learn something from it or not. What we learn from this discussion are several things;

First, Bat's observations and Phil's solution are not in conflict.
Second, if you make an invalid assumption and see what a chain says about it, you may (probably will) get contradictions. That doesn't mean that the chain is wrong. If the chain has been done right it means that the assumption is wrong, and that will probably give you progress in solving the puzzle.
Third, by looking at how the contradictions arise, you may get an idea for another solution. I did in this case, though it was only slightly shorter than Phil's original.

[bat999]

...you and Phil are both right; you've just expressed the answer differently...
... Bat's observations and Phil's solution are not in conflict....

Yup.

One method uses a pincer attack to determine that r8c5<>3 if r2c5=3 and r8c5<>3 if r2c5<>3.
One method uses logic to determine that r2c5=3.