The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.2.|...|
 |.3.|..5|..4|
 |7..|1.6|...|
 |---+---+---|
 |..6|28.|...|
 |.5.|...|2.8|
 |8..|.3.|..6|
 |---+---+---|
 |...|8.3|.4.|
 |...|...|79.|
 |.17|6..|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*---------------------------------------------*
| 1569 b469  a1459 | 3 2 8   | 159   1567 79  |
| 126   3     128  | 7 9 5   | 18    1268 4   |
| 7     289   2589 | 1 4 6   | 3589  2358 239 |
|------------------+---------+----------------|
| 139   479   6    | 2 8 147 | 13459 1357 379 |
| 13    5    f13-4 | 9 6 147 | 2     137  8   |
| 8     2479  1249 | 5 3 147 | 149   17   6   |
|------------------+---------+----------------|
| 259   29    259  | 8 7 3   | 6     4    1   |
|d36   c68   e38   | 4 1 2   | 7     9    5   |
| 4     1     7    | 6 5 9   | 38    238  23  |
*---------------------------------------------*

(4) r1c3 = (4-6) r1c2 = r8c2 - (6=3) r8c1 - r8c3 = (3) r5c3 => - 4 r5c3; stte

Leren

[SpAce]

Original: Show

Code: Select all

.----------------------.-----------.------------------.
| 1569  c469   c1(4)59 | 3  2  8   | 159    1567  79  |
| 126    3      128    | 7  9  5   | 18     1268  4   |
| 7      289    2589   | 1  4  6   | 3589   2358  239 |
:----------------------+-----------+------------------:
| 139    479    6      | 2  8  147 | 13459  1357  379 |
| 13     5     a1[3]-4 | 9  6  147 | 2      137   8   |
| 8      2479   1249   | 5  3  147 | 149    17    6   |
:----------------------+-----------+------------------:
| 259    29     259    | 8  7  3   | 6      4     1   |
| 36    b68    b38     | 4  1  2   | 7      9     5   |
| 4      1      7      | 6  5  9   | 38     238   23  |
'----------------------'-----------'------------------'

(3)r5c3 = (38-6)r8c32 = (64)r1c23 => -4 r5c3; stte

The first one was too similar to Leren's, so:

Code: Select all

.------------------------.-----------.------------------.
|    1569  c469   c1459  | 3  2  8   | 159    1567  79  |
|    126    3      128   | 7  9  5   | 18     1268  4   |
|    7      289    2589  | 1  4  6   | 3589   2358  239 |
:------------------------+-----------+------------------:
| ad(1+9)3  479    6     | 2  8  147 | 13459  1357  379 |
| ad(1)3    5     d(1)34 | 9  6  147 | 2      137   8   |
|    8      2479   249-1 | 5  3  147 | 149    17    6   |
:------------------------+-----------+------------------:
|    259    29     259   | 8  7  3   | 6      4     1   |
|   a36    b68     38    | 4  1  2   | 7      9     5   |
|    4      1      7     | 6  5  9   | 38     238   23  |
'------------------------'-----------'------------------'

(19=36)r458c1 - r8c2 = (64)r1c23 - (43=19)b4p641 => -1 r6c3, +9 r4c1; stte

Added. I don't think I've ever tried this before, but might the CoALS rule work here? Let's give it a shot:

CoALS workout: Show

ALS A: (1369)r458c1 (<-> b4p14,r8c1)
ALS B: (1349)b4p146
Combined structure: (13469)b4p146,r8c1
Overlap: (139)b4p14
Non-overlap: (46)b4p6,r8c1
CoALS rule: (139==46)b4p146,r8c1

(139==46)b4p146,r8c1 - (6)r8c2 = (64)r1c23 - (4=139)b4p146 => -1 b4p9, +9 b4p1; stte

(It's also easy to see that (46)b4p146,r8c1 can't be true because it produces a contradiction (4&6)r1c2, so (139) must be true.)

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 1569  b469   a1459   | 3      2      8      | 159    1567   79     |
 | 126    3      128    | 7      9      5      | 18     1268   4      |
 | 7      289    2589   | 1      4      6      | 3589   2358   239    |
 *----------------------+----------------------+----------------------|
 |d139   d479    6      | 2      8      147    | 13459  1357   379    |
 |d13     5      134    | 9      6      147    | 2      137    8      |
 | 8     d2479  d1249   | 5      3      147    | 149    17     6      |
 *----------------------+----------------------+----------------------|
 | 259    29     259    | 8      7      3      | 6      4      1      |
 |c36    b68     38     | 4      1      2      | 7      9      5      |
 | 4      1      7      | 6      5      9      | 38     238    23     |
 *--------------------------------------------------------------------*


4r1c3 = (46)r18c2 - (6=3)r8c1 - (3=12479)b4p12489 => -4 r5c3 ; stte

Yarg. Looks like another Leren copy.

[Sudtyro2]

Code: Select all

+--------------------+--------------+-------------------+
| b1569 469   b1459  | 3   2   8    | b159   1567  79  |
|  126  3      128   | 7   9   5    |  18    1268  4    |
|  7    289    2589  | 1   4   6    |  3589  2358  239  |
+--------------------+--------------+-------------------+
|  139  479    6     | 2   8   147  |  13459 1357  379  |
| a13   5     a134   | 9   6   147  |  2     137   8    |
|  8    2479   1249  | 5   3   147  |  149   17    6    |
+--------------------+--------------+-------------------+
|  259  29     259   | 8   7   3    |  6     4     1    |
| a36   68     38    | 4   1   2    |  7     9     5    |
|  4    1      7     | 6   5   9    |  38    238   23   |
+--------------------+--------------+-------------------+

Hi SpAce,
Here's a start to a simpler CoALS thanks to your reminder. The two (bi-cell) overlapping ALS are tagged(a).
(13=46) - (4|6=159)r1c137. The remaining 159NT is stte, but I don't have the equivalent stte elims stemming solely from the overlap cell. Any hope here?

SteveC

[SpAce]

Here's a start to a simpler CoALS thanks to your reminder. The two (bi-cell) overlapping ALS are tagged(a).
(13=46) - (4|6=159)r1c137. The remaining 159NT is stte, but I don't have the equivalent stte elims stemming solely from the overlap cell. Any hope here

Hi Steve! I'm glad you chimed in, as you're the resident CoALS expert! If it weren't for you, I probably wouldn't even know about the CoALS rule. Your example is indeed simpler. I'd use the same logic as before, however, and I don't see any other easy way (*):

ALS A: (136)r58c1
ALS B: (134)r5c13
Combined structure: (1346)r58c1,r5c3
Overlap: (13)r5c1
Non-overlap: (46)r5c3,r8c1
CoALS rule: (13==46)r58c1,r5c3

One way to use it is to see the contradiction with the (46) option, which rules it out:

(46)r58c1,r5c3 - (4|6)r1c3,r8c2 = (46!)r1c2 -> +(13)r58c1,r5c3 => -13 r4c1, -1 r6c3; stte

Or as an AIC:

(13==46)r58c1,r5c3 - (6)r8c2 = (64)r1c23 - (4=13)r5c13 => -13 r4c1, -1 r6c3; stte

or:

(13==64)r58c1,r5c3 - (4)r1c3 = (46)r18c2 - (6=31)r85c1 => -13 r4c1, -1 r6c3; stte

However, those AICs only use one of the (46) digits for linking (like my original), which suggests we could drop the CoALS rule here and simply use the ALSs directly:

(13=6)r58c1 - r8c2 = (64)r1c23 - (4=13)r5c13 => -13 r4c1, -1 r6c3; stte

...which I think would be the best option.

(*) It's of course possible to use the equivalent naked set as well, as you suggested, but it's unnecessarily complex:

(13==64)r58c1,r5c3 - (6|4=9157)r1c1379 - (1|5|7=6)r1c8 - r1c2 = r8c2 - (6=31)r85c1 => -13 r4c1, -1 r6c3; stte

I guess we get the best payoff with CoALS when multiple digits actually need to be used for linking, or otherwise simpler options exist. Here only the contradiction solution and the complex AIC use both digits (4 and 6) so they're actually more in line with the CoALS spirit than the simpler AICs. So, my conclusion is that CoALS is probably impractical (too complicated) for this situation (just like my own), but the principles still hold, and it's best to start learning new things with simple examples!

PS. Related to a different discussion and topic, this is a good example of why I advocate marking placements with the '+' notation instead of as eliminations. As I said there:

When a chain indicates that a direct placement is available, the most efficient option is almost always (here as well) to shorten the chain and show an elimination. But, for that reason too I think it's a good habit to show placements when available, because it alerts to the fact that there's probably a shorter chain available with the same effect.

Here my solution included a placement:

(19=36)r458c1 - r8c2 = (64)r1c23 - (43=19)b4p641 => -1 r6c3, +9 r4c1; stte

Had I (fully) followed my own advice, I would have looked for this simpler option right away:

(13=6)r58c1 - r8c2 = (64)r1c23 - (4=13)r5c13 => -13 r4c1, -1 r6c3; stte

For some unknown reason I didn't until I saw your comment (But at least the hint was there!)

[Sudtyro2]

Hi SpaCe,
Wow! Your extensive and thorough feedback is very much appreciated! I have learned a lot more now about how to find the CoALS "common outcome" needed for the stte solution. As you could tell, I simply bogged down at the 159NT in r1. And I do also fully agree with your placement suggestion.

SteveC

[SpAce]

Wow! Your extensive and thorough feedback is very much appreciated! I have learned a lot more now about how to find the CoALS "common outcome" needed for the stte solution.

It's always great when both sides learn something new! You obviously have a better eye for potential CoALS situations, so keep them coming and we can learn more! While they can be used to build AICs, I don't think it's terrible to use them to produce contradictions either -- as long as achieving one is quite obvious and doesn't require long chains. Some of Myth's examples are much simpler as immediate contradictions than AICs (which require pretty hefty split-nodes). The contradiction for our example is not immediate (requires an extra link) but it's still simpler than the AIC and more in line with the CoALS spirit (using both digits). So, CoALS may be a rare exception where I wouldn't mind seeing (or using) a contradiction solution.

As you could tell, I simply bogged down at the 159NT in r1.

I don't blame you. The NT was nicely revealed by using the full CoALS rule, so it was a good start. Too bad it had no linking potential.

And I do also fully agree with your placement suggestion.

Glad to hear!