The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.56|8..|
 |..1|2..|.9.|
 |.84|...|..5|
 |---+---+---|
 |45.|...|..3|
 |7..|...|.46|
 |...|...|.1.|
 |---+---+---|
 |8..|...|23.|
 |.3.|..1|...|
 |..7|9..|...|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.----------.--------------------.-------------.
| 9  7  3  |  1     5     6     |   8    2  4 |
| 5  6  1  |  2     48    48    |   3    9  7 |
| 2  8  4  | c3(7)  379   379   |   1    6  5 |
:----------+--------------------+-------------:
| 4  5  26 |  6-7   1     29-7  | a[7]9  8  3 |
| 7  1  28 | b35    389   23589 |   59   4  6 |
| 3  9  68 |  4     678  b578   |  a57   1  2 |
:----------+--------------------+-------------:
| 8  4  9  |  567   67   c5(7)  |   2    3  1 |
| 6  3  5  |  8     2     1     |   4    7  9 |
| 1  2  7  |  9     34    34    |   6    5  8 |
'----------'--------------------'-------------'


(75)r46c7 = (53)b5p94 - (5|3=7)r7c6&r3c4 => -7 r4c46; stte

[ArkieTech]

Code: Select all

.----------.--------------------.-------------.
| 9  7  3  |  1     5     6     |   8    2  4 |
| 5  6  1  |  2     48    48    |   3    9  7 |
| 2  8  4  | c3(7)  379   379   |   1    6  5 |
:----------+--------------------+-------------:
| 4  5  26 |  6-7   1     29-7  | a[7]9  8  3 |
| 7  1  28 | b35    389   23589 |   59   4  6 |
| 3  9  68 |  4     678  b578   |  a57   1  2 |
:----------+--------------------+-------------:
| 8  4  9  |  567   67   c5(7)  |   2    3  1 |
| 6  3  5  |  8     2     1     |   4    7  9 |
| 1  2  7  |  9     34    34    |   6    5  8 |
'----------'--------------------'-------------'


(75)r46c7 = (53)b5p94 - (5|3=7)r7c6&r3c4 => -7 r4c46; stte

Nice

[Ngisa]

Code: Select all

+----------------+-----------------------+----------------+
| 9     7     3  |  1      5       6     | 8      2     4 |
| 5     6     1  |  2      48      48    | 3      9     7 |
| 2     8     4  | b37    c37*9    379   | 1      6     5 |
+----------------+-----------------------+----------------+
| 4     5     26 | b67     1       279   |f7-9    8     3 |
| 7     1     28 | a35     389     23589 |a59     4     6 |
| 3     9     68 |  4     d678     578   |e57     1     2 |
+----------------+-----------------------+----------------+
| 8     4     9  |bc567   c67*     57    | 2      3     1 |
| 6     3     5  |  8      2       1     | 4      7     9 |
| 1     2     7  |  9      34      34    | 6      5     8 |
+----------------+-----------------------+----------------+


(9=53)r5c47 - (3=765)r347c4 - (7*)r3c5&(67*)r7c45 = (7)r6c5 - r6c7 = (7)r4c7 => 9r4c7; stte

Clement

[Cenoman]

(75)r46c7 = (53)b5p94 - (5|3=7)r7c6&r3c4 => -7 r4c46; stte

Tricky and nice !

An almost one-step AIC:

Code: Select all

 +-----------------+----------------------+-----------------+
 |  9    7    3    |  1     5     6       |  8    2    4    |
 |  5    6    1    |  2     48    48      |  3    9    7    |
 |  2    8    4    |  37    379   379     |  1    6    5    |
 +-----------------+----------------------+-----------------+
 |  4    5    26   | g6-7   1     29-7    | a79   8    3    |
 |  7    1    28   |  35    389   23589   |  59   4    6    |
 |  3    9    68   |  4    f678  c578     | b57   1    2    |
 +-----------------+----------------------+-----------------+
 |  8    4    9    |  567  e67   d57      |  2    3    1    |
 |  6    3    5    |  8     2     1       |  4    7    9    |
 |  1    2    7    |  9     34    34      |  6    5    8    |
 +-----------------+----------------------+-----------------+

(7)r4c7 = (7-5)r6c7 = r6c6 - (5=7)r7c6* - (7=6)r7c5 - r7c4 = (6)r4c4 => -7 r4c4, r4c6*; ste

[eleven]

Code: Select all

 *--------------------------------------------------*
 |  9  7  3    |  1     5     6       |  8    2  4  |
 |  5  6  1    |  2     48    48      |  3    9  7  |
 |  2  8  4    |  37    379   379     |  1    6  5  |
 |-------------+----------------------+-------------|
 |  4  5  26   | a67    1     29-7    |  79   8  3  |
 |  7  1  28   |  35    389   23589   |  59   4  6  |
 |  3  9 b68   |  4    b78-6 b578     |  57   1  2  |
 |-------------+----------------------+-------------|
 |  8  4  9    |  567  c67   c57      |  2    3  1  |
 |  6  3  5    |  8     2     1       |  4    7  9  |
 |  1  2  7    |  9     34    34      |  6    5  8  |
 *--------------------------------------------------*

(6=7)r4c4 - (7=5)r6c356 - (5=76)r7c65 => -6r6c5,-7r4c6; stte
Better (6,7)r3c4,r6c56 = 5r6c356 - (5=76)r7c56 ?
[Edit: corrected typo, thanks Cenoman]

[SpAce]

Nice

Tricky and nice !

Thanks, guys! Not really sure if the last term is strictly speaking correct as written, but I'm glad it got understood anyway

[SpAce]

(6=7)r3c4 - (7=5)r6c356 - (5=76)r7c65 => -6r6c5,-7r4c6; stte
Better (6,7)r3c4,r6c56 = 5r6c356 - (5=76)r7c56 ?

Hi eleven! I really like the logic, but both of those are a bit hard to read (for me). I also can't seem to find much better notations for the exact same logic. I found this instead:

(67)r4c47 = (7,5)r6c76 - (5=76)r7c65 => -6 r6c5,r7c4, -7 r4c6

Would that work for you?

[ArkieTech]

Code: Select all

 *--------------------------------------------------*
 |  9  7  3    |  1     5     6       |  8    2  4  |
 |  5  6  1    |  2     48    48      |  3    9  7  |
 |  2  8  4    |  37    379   379     |  1    6  5  |
 |-------------+----------------------+-------------|
 |  4  5  26   | a67    1     29-7    |  79   8  3  |
 |  7  1  28   |  35    389   23589   |  59   4  6  |
 |  3  9 b68   |  4    b78-6 b578     |  57   1  2  |
 |-------------+----------------------+-------------|
 |  8  4  9    |  567  c67   c57      |  2    3  1  |
 |  6  3  5    |  8     2     1       |  4    7  9  |
 |  1  2  7    |  9     34    34      |  6    5  8  |
 *--------------------------------------------------*

(6=7)r3c4 - (7=5)r6c356 - (5=76)r7c65 => -6r6c5,-7r4c6; stte
Better (6,7)r3c4,r6c56 = 5r6c356 - (5=76)r7c56 ?

[(7|6=5)r4c4,r6c356-(5=76)r7c65]-7r4c6,-6r6c5; ste
??

[eleven]

(67)r4c47 = (7,5)r6c76 - (5=76)r7c65 => -6 r6c5,r7c4, -7 r4c6

Would that work for you?

Nice, too (like your first one).

[Cenoman]

Not really sure if the last term is strictly speaking correct as written, but I'm glad it got understood anyway

Don't know either if the last term is not correct as written. The ste finish needs both eliminations, therefore the last node in this last term shall be (7)r7c6&r3c4.
Not obvious how to interpret the middle weak link: (53)b5p94 - (5|3)r7c6&r3c4

it got understood anyway

Sure, but not easily.
As I often do, I have rewritten it my way

Code: Select all

(7)r4c7 = (7-5)r6c7 =  (5)r6c6  - (5=3)r5c4 - (3=7)r3c4
                                              \ (5=7)r7c6

You chose to group the term (5=3)r5c4 with 5r6c6. I would group it with (3=7)r3c4, getting the ALS (5=37)r35c4.
For once, if you accept to omit the bystander you could write the whole thing (7)r4c7 = (7-5)r6c7 = (5)r6c6 - (5=7)r35c4&r7c6

Side remark: not easy to put this double chain into a matrix.

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 | 9      7      3      | 1      5      6      |  8      2      4      |
 | 5      6      1      | 2      48     48     |  3      9      7      |
 | 2      8      4      | 37     379    379    |  1      6      5      |
 *----------------------+----------------------+-----------------------|
 | 4      5      26     | 67     1     c279    |  79     8      3      |
 | 7      1      28     |c35    c389   c23589  |  59     4      6      |
 | 3      9      68     | 4     c678    78-5   |ab57     1      2      |
 *----------------------+----------------------+-----------------------|
 | 8      4      9      | 567   b67   ab57     |  2      3      1      |
 | 6      3      5      | 8      2      1      |  4      7      9      |
 | 1      2      7      | 9      34     34     |  6      5      8      |
 *---------------------------------------------------------------------*


5r6c7,r7c6 = 7r6c7&(67)r7c56 - (6|7=23895)b5p34568 => -5 r6c6 ; stte

[SteveG48]

Thanks, guys! Not really sure if the last term is strictly speaking correct as written, but I'm glad it got understood anyway

I like your solution too.

If we try to expand the last term, it gets awkward, so I'd split it into two: 5r7c6|3r3c4 = 7r7c6&r3c4 .

[Cenoman]

(6=7)r4c4 - (7=5)r6c356 - (5=76)r7c65 => -6r6c5,-7r4c6; stte
Better (6,7)r4c4,r6c56 = 5r6c356 - (5=76)r7c56 ?

Same kind of comments. This is hard to read. Both eliminations are needed for the ste finish.
I'd stick to the developed form: (6=7)r4c4 - *(7=685)r6c356 - (5=7)r7c6* - (7=6) r7c5 => -7 r4c6*, -6 r6c5
Just a matter of taste and colours...

Same side remark as to SpAce: this chain with embedded subchain is hard to put into a matrix (as well as my own, BTW)

[SpAce]

Don't know either if the last term is not correct as written. The ste finish needs both eliminations, therefore the last node in this last term shall be (7)r7c6&r3c4.
Not obvious how to interpret the middle weak link: (53)b5p94 - (5|3)r7c6&r3c4

If we try to expand the last term, it gets awkward, so I'd split it into two: 5r7c6|3r3c4 = 7r7c6&r3c4 .

I hear both of you. I knew it was questionable when I wrote it, but did it anyway for aesthetic reasons But, like Cenoman, I'm not really sure if it's truly incorrect either. Seems more like undefined (which I guess is pretty much the same thing, though).

You chose to group the term (5=3)r5c4 with 5r6c6. I would group it with (3=7)r3c4, getting the ALS (5=37)r35c4.

I actually used that grouping in my first draft:

(7)r4c7 = (7,5)r6c76 - (5)r5c4|r7c6 = (37)r53c4&(7)r7c6 => -7 r4c46

For once, if you accept to omit the bystander you could write the whole thing (7)r4c7 = (7-5)r6c7 = (5)r6c6 - (5=7)r35c4&r7c6

Uncharacteristically, I did consider that, too! It's actually what got me thinking about using the questionable &-term at the end.

Side remark: not easy to put this double chain into a matrix.

Yes, it's often the case with these when you need an ANDed end point. This doesn't seem like the worst of its kind, though:

Code: Select all

 7r4c7       7r6c7
             5r6c7 5r6c6
                   5r5c4 3r5c4
 7r7c6&7r3c4       5r7c6 3r3c4
------------------------------
-7r4c46

Would you accept that?