The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.9.|.36|...|
 |.74|.8.|...|
 |5.2|1..|...|
 |---+---+---|
 |9..|86.|.2.|
 |2..|...|..6|
 |.1.|.47|..5|
 |---+---+---|
 |...|..9|6.8|
 |...|.7.|59.|
 |...|31.|.4.|
 *-----------*


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[eleven]

xy-chain or:

Code: Select all

 *----------------------------------------------------------*
 |  1    9     8     |  7  3  6    |  24      5      24     |
 |  36   7     4     |  5  8  2    |  13      136    9      |
 |  5    6-3   2     |  1  9  4    |  378     3678  a37     |
 |-------------------+-------------+------------------------|
 |  9    345  *357   |  8  6  13   | #1347    2     #1347   |
 |  2    348  b37    |  9  5  13   |  13478   1378   6      |
 |  38   1     6     |  2  4  7    |  9       38     5      |
 |-------------------+-------------+------------------------|
 |  7   d35   c135   |  4  2  9    |  6       13     8      |
 |  4    2    c13    |  6  7  8    |  5       9      13     |
 |  68   68    9     |  3  1  5    | #27      4     #27     |
 *----------------------------------------------------------*

xwing 7r49c79 = 7r4c3
(3=7)r3c9-x-wing=7r4c3-(7=3)r5c3-r78c3=r7c2 => -3r3c2, stte
or (3=7)r3c9-x-wing=(7-5)r4c3=r4c2-(5=3)r7c2 => -3r3c2, stte

[pjb]

Code: Select all

 1       9       8      | 7      3      6      | 24     5      24     
a36      7       4      | 5      8      2      | 13    b136    9     
 5       36      2      | 1      9      4      | 378   c3678   37     
------------------------+----------------------+---------------------
 9       345     357    | 8      6      13     | 1347   2      1347   
 2       348    e37     | 9      5      13     | 13478 d1378   6     
 8-3     1       6      | 2      4      7      | 9      38     5     
------------------------+----------------------+---------------------
 7       35      135    | 4      2      9      | 6      13     8     
 4       2       13     | 6      7      8      | 5      9      13     
 68      68      9      | 3      1      5      | 27     4      27     


(3=6)r2c1 - r2c8 = (6-7)r3c8 = r5c8 - (7=3)r5c3 => -3 r6c1; stte

Phil

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 1      9      8      | 7      3      6      | 24     5      24     |
 |b36     7      4      | 5      8      2      | 13     136    9      |
 | 5     a36     2      | 1      9      4      | 378    3678   7-3    |
 *----------------------+----------------------+----------------------|
 | 9      345    357    | 8      6      13     | 1347   2      1347   |
 | 2      348    37     | 9      5      13     | 13478  1378   6      |
 |c38     1      6      | 2      4      7      | 9     d38     5      |
 *----------------------+----------------------+----------------------|
 | 7      35     135    | 4      2      9      | 6     d13     8      |
 | 4      2      13     | 6      7      8      | 5      9     e13     |
 | 68     68     9      | 3      1      5      | 27     4      27     |
 *--------------------------------------------------------------------*


3r3c2 = r2c1 - (3=8)r6c1 - (8=13)r67c8 - (1=3)r8c9 => -3 r3c9 ; stte

[Marty R.]

Code: Select all

+------------+--------+-----------------+
| 1  9   8   | 7 3 6  | 24    5    24   |
| 36 7   4   | 5 8 2  | 13    136  9    |
| 5  36  2   | 1 9 4  | 378   3678 37   |
+------------+--------+-----------------+
| 9  345 357 | 8 6 13 | 1347  2    1347 |
| 2  348 37  | 9 5 13 | 13478 1378 6    |
| 38 1   6   | 2 4 7  | 9     38   5    |
+------------+--------+-----------------+
| 7  35  135 | 4 2 9  | 6     13   8    |
| 4  2   13  | 6 7 8  | 5     9    13   |
| 68 68  9   | 3 1 5  | 27    4    27   |
+------------+--------+-----------------+


Play this puzzle online at the Daily Sudoku site

3r2c1=r6c1-(3=4578)b4p2356-(78=13867)r56723c8-(7=3)r3c9=> -3r3c2

[Ngisa]

Code: Select all

+----------------------+------------------+---------------------------+
| 1       9        8   | 7      3      6  | 24         5         24   |
|h36      7        4   | 5      8      2  | 13        g136       9    |
| 5       36       2   | 1      9      4  | 378       f3678      37   |
+----------------------+------------------+---------------------------+
| 9       345     c357 | 8      6      13 | 1347       2         1347 |
| 2       348     d37  | 9      5      13 | 13478     e1378      6    |
|i38      1        6   | 2      4      7  | 9         j38        5    |
+----------------------+------------------+---------------------------+
| 7       35      b135 | 4      2      9  | 6        ka1-3        8   |
| 4       2        13  | 6      7      8  | 5          9         13   |
| 68      68       9   | 3      1      5  | 27         4         27   |
+----------------------+------------------+---------------------------+


(1)r7c8 = (1-5)r7c3 = (5-7)r4c3 = r5c3 - r5c8 = (7-6)r3c8 = r2c8 - (6=3)r2c1 - (3=8)r6c1 - (8=3)r6c8 - (3=1)r7c8 => -3 r7c8; stte

Clement

[SteveG48]

Code: Select all

+------------+--------+-----------------+
| 1  9   8   | 7 3 6  | 24    5    24   |
| 36 7   4   | 5 8 2  | 13    136  9    |
| 5  36  2   | 1 9 4  | 378   3678 37   |
+------------+--------+-----------------+
| 9  345 357 | 8 6 13 | 1347  2    1347 |
| 2  348 37  | 9 5 13 | 13478 1378 6    |
| 38 1   6   | 2 4 7  | 9     38   5    |
+------------+--------+-----------------+
| 7  35  135 | 4 2 9  | 6     13   8    |
| 4  2   13  | 6 7 8  | 5     9    13   |
| 68 68  9   | 3 1 5  | 27    4    27   |
+------------+--------+-----------------+


Play this puzzle online at the Daily Sudoku site

3r2c1=r6c1-(3=4578)b4p2356-(78=13867)r56723c8-(7=3)r3c9=> -3r3c2

Marty, unfortunately, in the step I've highlighted, you don't know whether the 7 is in r4c3 or r5c3, so you can't make the next step eliminating the 7 at r5c8.

[Cenoman]

Code: Select all

 +-------------------+-----------------+------------------------+
 |  1    9     8     |  7    3    6    |  24      5      24     |
 | b36   7     4     |  5    8    2    |af13     a136    9      |
 |  5    36    2     |  1    9    4    | f378     678-3  7-3    |
 +-------------------+-----------------+------------------------+
 |  9    345   357   |  8    6    13   | e1347    2      1347   |
 |  2    348   37    |  9    5    13   | e13478   1378   6      |
 | c38   1     6     |  2    4    7    |  9      d38     5      |
 +-------------------+-----------------+------------------------+
 |  7    35    135   |  4    2    9    |  6       13     8      |
 |  4    2     13    |  6    7    8    |  5       9      13     |
 |  68   68    9     |  3    1    5    |  27      4      27     |
 +-------------------+-----------------+------------------------+

Simple Coloring: (3)r2c78 = r2c1 - r6c1 = r6c8 - r45c7 = r23c7 => -3 r3c89; stte

[Marty R.]

Code: Select all

+------------+--------+-----------------+
| 1  9   8   | 7 3 6  | 24    5    24   |
| 36 7   4   | 5 8 2  | 13    136  9    |
| 5  36  2   | 1 9 4  | 378   3678 37   |
+------------+--------+-----------------+
| 9  345 357 | 8 6 13 | 1347  2    1347 |
| 2  348 37  | 9 5 13 | 13478 1378 6    |
| 38 1   6   | 2 4 7  | 9     38   5    |
+------------+--------+-----------------+
| 7  35  135 | 4 2 9  | 6     13   8    |
| 4  2   13  | 6 7 8  | 5     9    13   |
| 68 68  9   | 3 1 5  | 27    4    27   |
+------------+--------+-----------------+


Play this puzzle online at the Daily Sudoku site

3r2c1=r6c1-(3=4578)b4p2356-(78=13867)r56723c8-(7=3)r3c9=> -3r3c2

Marty, unfortunately, in the step I've highlighted, you don't know whether the 7 is in r4c3 or r5c3, so you can't make the next step eliminating the 7 at r5c8.

Steve,

Yes. I am aware of that, with multiple instances of a number in an ALS, you don't know which it would be. Here's my story. I did that step mentally, going from b4p76325; 3-7-5-4-8 and then tried to minimize the notation by throwing it all into the one ALS. My alternate notation: 3r2c1=r6c1-(3=7)r5c3-(7=3458)r4c32,r5c2. That last term violates the rule of N-1 cells and I don't know why. But I think that when you do it mentally or plot it on a blank grid, r5c2-r5c3 must = 8-7. This is a frequent problem for me, plotting out results on a blank grid and then trying to figure out how to notate it.

[Cenoman]

r5c2-r5c3 must = 8-7

That's true:

Code: Select all

              8r6c1 = 8r5c2
             /
3r2c1 = 3r6c1
             \
              (3=7)r5c3

But as the end of your chain is something like ....(7)r3c8 - (7=3)r3c9 => -3r3c9
why wouldn't you connect the bottom part of this net with the native strong link 7r5c8 = 7r3c8 in column 8 [as your link(78=13867)r56723c8] ?
You would then get the very simple chain:

(3)r2c1 = r6c1 - (3=7)r5c3 - r5c8 = r3c8 - (7=3)r3c9 => -3r3c9

[Marty R.]

r5c2-r5c3 must = 8-7

That's true:

Code: Select all

              8r6c1 = 8r5c2
             /
3r2c1 = 3r6c1
             \
              (3=7)r5c3

But as the end of your chain is something like ....(7)r3c8 - (7=3)r3c9 => -3r3c9
why wouldn't you connect the bottom part of this net with the native strong link 7r5c8 = 7r3c8 in column 8 [as your link(78=13867)r56723c8] ?
You would then get the very simple chain:

(3)r2c1 = r6c1 - (3=7)r5c3 - r5c8 = r3c8 - (7=3)r3c9 => -3r3c9

Cenoman,

Thanks, input is always welcome and appreciated. Your "very simple chain" is obviously vastly superior. and I'm sorry that I didn't see it. I don't understand some of the terminology. I don't know what a net is nor do I know the difference between a strong link and "native" strong link.

[Cenoman]

I don't understand some of the terminology. I don't know what a net is nor do I know the difference between a strong link and "native" strong link.

A net in sudoku is a complex chain made of several crossing lines: it starts when you need to split one chain into two sub-chains to display a weak or a strong link between 3 candidates or groups of candidates. This my personal understanding. Don't know if there is an "official" definition somewhere.

My preferred definition of a strong link is: "candidates are strongly linked when one at least must be true", equivalent to the boolean equation a OR b OR c OR ... = TRUE
In my mind, native strong links are such strong links directly inferred from sudoku rules, i.e. strong links that you can see on the grid of candidates. The other strong links are derived from diverse patterns as ALS's, AIC's, DP's, ... I sometimes use the symbol "==" for derived strong links (to warn the reader not to search for them on the grid)
Note that derived strong links meet the same boolean equation as written above.