The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8.1|6..|2..|
 |...|...|..3|
 |574|...|...|
 |---+---+---|
 |..5|.12|.84|
 |...|.7.|...|
 |42.|36.|1..|
 |---+---+---|
 |...|...|479|
 |9..|...|...|
 |..3|..4|8.1|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 8       3       1      | 6      45     79     | 2      49     57     
 26      9       26     | 58     458    17     | 57     14     3     
 5       7       4      | 12     23     139    | 69     169    8     
------------------------+----------------------+---------------------
a37      6       5      | 9      1      2      |b37     8      4     
 13      18      89     | 4      7      58     | 69    c23569  26     
 4       2       789    | 3      6      58     | 1      59     57     
------------------------+----------------------+---------------------
 126     18      268    | 258    2358   36     | 4      7      9     
 9       4       2678   | 1278   28     16     | 35     35     26     
 26-7    5       3      |e27     9      4      | 8     d26     1     


(7=3)r4c1 - r4c7 = (3-2)r5c8 = r9c8 - (2=7)r9c4 => -7 r9c1; stte

Phil

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 8      3      1      | 6     g45     79     | 2    ag49    g57     |
 | 26     9      26     | 58     458    17     | 57    a14     3      |
 | 5      7      4      | 12     23     139    | 69    a169    8      |
 *----------------------+----------------------+----------------------|
 | 37     6      5      | 9      1      2      | 37     8      4      |
 | 13     18     89     | 4      7      58     | 69     2356-9 26     |
 | 4      2     e789    | 3      6      58     | 1      5-9   f57     |
 *----------------------+----------------------+----------------------|
 | 126    18     268    | 258    2358   36     | 4      7      9      |
 | 9      4     d2678   | 1278   28     16     | 35     35     26     |
 |c267    5      3      |b27     9      4      | 8     a26     1      |
 *--------------------------------------------------------------------*


(9=1462)r1239c8 - (2=7)r9c4 - r9c1 = r8c3 - r6c3 = r6c9 - (7=459)r1c589 => -9 r56c8 ; stte

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 8       3       1        | 6       45      79       | 2       49      57       |
| 26      9       26       | 58      458     17       | 57      14      3        |
| 5       7       4        | 12      23      139      | 69      169     8        |
|--------------------------+--------------------------+--------------------------|
|b37      6       5        | 9       1       2        |a37      8       4        |
| 13      18      89       | 4       7       58       | 69     f2569-3  26       |
| 4       2       789      | 3       6       58       | 1       59      57       |
|--------------------------+--------------------------+--------------------------|
| 126     18      268      | 258     2358    36       | 4       7       9        |
| 9       4       2678     | 1278    28      16       | 35      35      26       |
|c267     5       3        |d27      9       4        | 8      e26      1        |
*--------------------------------------------------------------------------------*

(3) r4c7 = (3-7) r4c1 = r9c1 - (7=2) r9c4 - r9c8 = (2) r5c8 => - 3 r5c8; stte

Leren

[bat999]

Code: Select all

.----------------.-------------------.------------------.
|  8    3   1    |  6     45     79  |  2    49     57  |
|  26   9   26   |  58    458   a17  | b57   14     3   |
|  5    7   4    |  12    23     139 |  69   169    8   |
:----------------+-------------------+------------------:
| d37   6   5    |  9     1      2   | c37   8      4   |
|  13   18  89   |  4     7      58  |  69   23569  26  |
|  4    2   789  |  3     6      58  |  1    59     57  |
:----------------+-------------------+------------------:
|  126  18  268  |  258   2358   36  |  4    7      9   |
|  9    4   2678 |  1278  28    a16  |  35   35     2-6 |
| e267  5   3    | f27    9      4   |  8   f26     1   |
'----------------'-------------------'------------------'

(6=7)r28c6 - r2c7 = r4c7 - r4c1 = r9c1 - (7=6)r9c48 => -6 r8c9; stte

[Marty R.]

Code: Select all

+-------------+---------------+-------------+
| 8   3  1    | 6    45   79  | 2  49    57 |
| 26  9  26   | 58   458  17  | 57 14    3  |
| 5   7  4    | 12   23   139 | 69 169   8  |
+-------------+---------------+-------------+
| 37  6  5    | 9    1    2   | 37 8     4  |
| 13  18 89   | 4    7    58  | 69 23569 26 |
| 4   2  789  | 3    6    58  | 1  59    57 |
+-------------+---------------+-------------+
| 126 18 268  | 258  2358 36  | 4  7     9  |
| 9   4  2678 | 1278 28   16  | 35 35    26 |
| 267 5  3    | 27   9    4   | 8  26    1  |
+-------------+---------------+-------------+


Play this puzzle online at the Daily Sudoku site

6r9c8=(6-7)r9c1=r4c1-(7=3)r4c7-(3=57)r82c7-(7=149)r2c6,b3p52-(9=6)r3c7=> -6r3c8

[Marty R.]

Code: Select all

 *--------------------------------------------------------------------*
 | 8      3      1      | 6     g45     79     | 2    ag49    g57     |
 | 26     9      26     | 58     458    17     | 57    a14     3      |
 | 5      7      4      | 12     23     139    | 69    a169    8      |
 *----------------------+----------------------+----------------------|
 | 37     6      5      | 9      1      2      | 37     8      4      |
 | 13     18     89     | 4      7      58     | 69     2356-9 26     |
 | 4      2     e789    | 3      6      58     | 1      5-9   f57     |
 *----------------------+----------------------+----------------------|
 | 126    18     268    | 258    2358   36     | 4      7      9      |
 | 9      4     d2678   | 1278   28     16     | 35     35     26     |
 |c267    5      3      |b27     9      4      | 8     a26     1      |
 *--------------------------------------------------------------------*


(9=1462)r1239c8 - (2=7)r9c4 - r9c1 = r8c3 - r6c3 = r6c9 - (7=459)r1c589 => -9 r56c8 ; stte

Steve, I'm having trouble with the notation, specifically with term #1. I'm too weak on ALS's . I think to fit the solution, the non-9 needs to be r3c8, but how would I know that from just looking at the term, which includes two 9s?

[Ngisa]

Code: Select all

+-------------+---------------+-------------+
| 8   3  1    | 6    f45   79  | 2  f49    f57 |
| 26  9  26   | 1578 458  17  | 57 14    3  |
| 5   7  4    | 12   23   139 | g69 16-9   8  |
+-------------+---------------+-------------+
| 37  6  5    | 9    1    2   | 37 8     4  |
| 13  18 89   | 4    7    58  | 69 23569 26 |
| 4   2  d789  | 3    6    58  | 1  59    e57 |
+-------------+---------------+-------------+
| 126 18 268  | 258  2358 36  | 4  7     9  |
| 9   4  c2678 | 1278 28   167 | 35 35    26 |
| b267 5  3    | 27   9    4   | 8  a26    1  |
+-------------+---------------+-------------+


(6)r9c8=(6-7)r9c1=r8c3-r6c3=r6c9-(7=459)r1c589-(9=6)r3c7 => -6r3c8; stte

Clement

[eleven]

6r9c8=(6-7)r9c1=r4c1-(7=3)r4c7-(3=57)r82c7-(7=149)r2c6,b3p52-(9=6)r3c7=> -6r3c8

Marty,

do you mean that construct ironically ?


ALS just means, that you have n+1 candidates in n cells in one unit (i.e row/box/column), here in Steve's one 12469 in cells r1239c8.
If one of the candidates is missing in those cells, all others must be true. So if not one of r13c8 is 9, the 2 in r9c8 must be true (along with 146 in that cells 1239c8) and vice versa.

Difficult is, to find ALS's which really help you, there are many, as there are many bivalue cells, bilocation cells etc.

[bat999]

... I'm having trouble with the notation, specifically with term #1...

(9=1462)r1239c8
I take this to mean "If there isn't a 9 in any of r1c8 or r2c8 or r3c8 or r9c8 then there is a 2 in one of r1c8 or r2c8 or r3c8 or r9c8 (and also one of each 1,4,6)".

But it's a strange one...
(9=1462)r1239c8 - (2=7)r9c4 - r9c1 = r8c3 - r6c3 = r6c9 - (7=459)r1c589
This seems to say "If there isn't a 9 in any of r1c8 or r2c8 or r3c8 or r9c8 then through the chain it forces a 9 into one of r1c5 or r1c8 or r1c9".
So there is a 9 in one of r1c8 or r2c8 or r3c8 or r9c8 after all (it's r1c8) and we can eliminate -9 r56c8 (also -9 r3c7 imho).

I think this does the same job as a Type 2 Discontinuous Nice Loop.
"If the first square has two strong links with the same candidate, then it can be solved with the links' candidate".
In our case the "first square r1c8" is part of the "grouped node r1239c8".
The "link's candidate" is 9.
The first strong link (9=1462)r1239c8
The other strong link (7=459)r1c589

Probably Steve and others will see it completely differently, some kind of pincer maybe.
Gonna put my flak jacket on.

[eleven]

I dont' remember that nice loops dealt with ALS, but if you like, you can see it that way, the ALS's give the strong links 9r13c8=2r9c8 and 7r1c9=9r1c8. [Edit: probably it's not that nice loop type, 9r3c8 is not strongly linked to 7r1c9)

So you have a 9 in r13c8 or in r1c8, i.e. at least in one of r13c8 - and no one in r56c8 or r3c7.

[Marty R.]

(9=1462)r1239c8
I take this to mean "If there isn't a 9 in any of r1c8 or r2c8 or r3c8 or r9c8 then there is a 2 in one of r1c8 or r2c8 or r3c8 or r9c8 (and also one of each 1,4,6)".

I wasn't concerned with any of that other stuff, just wondering from looking at the 1st term, how I would've determined which was not true. I think it had to be r3c8 but that wasn't evident to me from looking at the ALS.

[bat999]

@eleven
...probably it's not that nice loop type, 9r3c8 is not strongly linked to 7r1c9)...
Maybe it's OK to link to only the 9r1c8 for the Nice Loop to work, but I'm not gonna argue about it.

@Marty R
I think it had to be r3c8...
No, that first term means none of r1c8 or r2c8 or r3c8 or r9c8 are 9.

[SteveG48]

But it's a strange one...
(9=1462)r1239c8 - (2=7)r9c4 - r9c1 = r8c3 - r6c3 = r6c9 - (7=459)r1c589
This seems to say "If there isn't a 9 in any of r1c8 or r2c8 or r3c8 or r9c8 then through the chain it forces a 9 into one of r1c5 or r1c8 or r1c9".
So there is a 9 in one of r1c8 or r2c8 or r3c8 or r9c8 after all (it's r1c8) and we can eliminate -9 r56c8 (also -9 r3c7 imho).

Yes! Well said, Bat.