The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..3|...|4..|
 |.1.|.5.|.2.|
 |7..|...|..6|
 |---+---+---|
 |9..|...|..8|
 |.3.|6.8|.5.|
 |..1|...|7..|
 |---+---+---|
 |..9|8.7|3..|
 |.6.|.2.|.4.|
 |...|9.5|...|
 *-----------*


Play/Print this puzzle online

[Cenoman]

Code: Select all

 +----------------------+-----------------------+-----------------------+
 |  258   259    3      |  12     18    6       |  4      1789   1579   |
 |  48    1      6      |  7      5     49      |  89     2      3      |
 |  7     2459   2458   |  1234   138   12349   |  1589   189    6      |
 +----------------------+-----------------------+-----------------------+
 |  9     2457   2457   |  1234   137   1234    |  6      13     8      |
 | a24    3      7-24   |  6      179   8       | d129    5    db1249   |
 |  6     8      1      |  5      39    24      |  7      39    c24     |
 +----------------------+-----------------------+-----------------------+
 |  1     25     9      |  8      4     7       |  3      6      25     |
 |  58    6      578    |  13     2     13      |  589    4      579    |
 |  3     247    2478   |  9      6     5       |  128    178    127    |
 +----------------------+-----------------------+-----------------------+

Loop (2=4)r5c1 - r5c9 = (4-2)r6c9 = (2)r5c79@ => -24 r5c3; ste

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 258    259    3      | 12     18     6      | 4      1789   1579   |
 | 48     1      6      | 7      5      49     | 89     2      3      |
 | 7      2459   2458   | 1234   138    12349  | 1589   189    6      |
 *----------------------+----------------------+----------------------|
 | 9      2457   2457   |d1234  d137   d1234   | 6     c13     8      |
 | 24     3      247    | 6    ae19-7   8      | 129    5      1249   |
 | 6      8      1      | 5     b39     24     | 7     c39     24     |
 *----------------------+----------------------+----------------------|
 | 1      25     9      | 8      4      7      | 3      6      25     |
 | 58     6      578    | 13     2      13     | 589    4      579    |
 | 3      247    2478   | 9      6      5      | 128    178    127    |
 *--------------------------------------------------------------------*


9r5c5 = r6c5 - (9=13)r46c8 - 1r4c456 = 1r5c5 => -7r5c5 ; stte

[SpAce]

Code: Select all

.-----------------.---------------------.-------------------.
| 258  259   3    |  12    18     6     | 4      1789  1579 |
| 48   1     6    |  7     5      49    | 89     2     3    |
| 7    2459  2458 |  1234  138    12349 | 1589   189   6    |
:-----------------+---------------------+-------------------:
| 9    2457  2457 | b1234  7-13  b1234  | 6     b13    8    |
| 24   3     247  |  6     179    8     | 129    5     1249 |
| 6    8     1    |  5     39    a24    | 7      39    24   |
:-----------------+---------------------+-------------------:
| 1    25    9    |  8     4      7     | 3      6     25   |
| 58   6     578  |  13    2      13    | 589    4     579  |
| 3    247   2478 |  9     6      5     | 128    178   127  |
'-----------------'---------------------'-------------------'

(2=4)r6c6 - (4=13'2)r4c468 - loop => -13 r4c5; stte

...aka Sue de Coq (classic variant)

...or yet another way to see it:

Code: Select all

.-----------------.------------------------.-------------------.
| 258  259   3    | 12       18    6       | 4      1789  1579 |
| 48   1     6    | 7        5     49      | 89     2     3    |
| 7    2459  2458 | 1234     138   12349   | 1589   189   6    |
:-----------------+------------------------+-------------------:
| 9    2457  2457 | 24+(13)  7-13  24+(13) | 6     (13)   8    |
| 24   3     247  | 6        179   8       | 129    5     1249 |
| 6    8     1    | 5        39    24+     | 7      39    24   |
:-----------------+------------------------+-------------------:
| 1    25    9    | 8        4     7       | 3      6     25   |
| 58   6     578  | 13       2     13      | 589    4     579  |
| 3    247   2478 | 9        6     5       | 128    178   127  |
'-----------------'------------------------'-------------------'

DP[24]b5p139 -> (13)r4c468 => -13 r4c5; stte

[SpAce]

What do you guys think of that somewhat unconventional DP-variant with the pseudo naked-pair? I think it's a pretty simple way to see and write the logic, similar to a UR Type 3. I'm thinking it might have some general utility as a simpler way to see some Sue de Coq and other doubly-linked ALS XZ situations, and possibly others. Works for Cenoman's solution as well:

Code: Select all

.------------------.------------------.-----------------------.
|  258  259   3    | 12    18   6     | 4       1789  1579    |
|  48   1     6    | 7     5    49    | 89      2     3       |
|  7    2459  2458 | 1234  138  12349 | 1589    189   6       |
:------------------+------------------+-----------------------:
|  9    2457  2457 | 1234  137  1234  | 6       13+   8       |
| (24)  3     7-24 | 6     179  8     | 19+(2)  5     19+(24) |
|  6    8     1    | 5     39   24    | 7       39+   24      |
:------------------+------------------+-----------------------:
|  1    25    9    | 8     4    7     | 3       6     25      |
|  58   6     578  | 13    2    13    | 589     4     579     |
|  3    247   2478 | 9     6    5     | 128     178   127     |
'------------------'------------------'-----------------------'

DP[139]b6p2846 -> (24)r5c179 => -24 r5c3; stte

Compare that to the corresponding Sue de Coq, doubly-linked ALS-XZ, or ALS loop. All are longer and more complex to write and understand, aren't they? What do you think?

Added. Cenoman's original can still be considered simpler (from one point of view at least) because its pattern uses one fewer cell and only deals with the digits 24. However, I guess we can think of the cell r6c9 as a single-cell DP (can't contain both 2 and 4) with externals (24)r5c79, which gives us the same pseudo-pair:

DP[2&4]r6c9 -> (24)r5c179 => -24 r5c3; stte

A bit weird, but logical? Another way to see it is to think of b6p469 as a pseudo-pair (24), which together with (24)r5c1 does the trick. Seems kind of patternish, no?

[SteveG48]

What do you guys think of that somewhat unconventional DP-variant with the pseudo naked-pair?

I like it.

Your original loop description seemed a bit confusing to me. I understood the eliminations, but I didn't understand how the loop gives rise to the them. I have some trouble at times figuring out the eliminations from a loop, but what I look for is weak links that become strong links giving the eliminations. I didn't see 1-3 weak links in your loop, so the eliminations weren't obvious from the description. It takes a second to "get" the DP description, but it works for me.

[SpAce]

I like it.

Great! Then I guess we should explore the idea more. I originally got it here, but it wasn't a great example as the chains got pretty complex (it got better with eleven's suggestion of using your elimination and chains, though).

Your original loop description seemed a bit confusing to me.

It's not exactly intuitive, is it? That was one reason that prompted me to look for alternatives. In general, most ALS loops take a while to digest, whether written as such or as doubly-linked ALS XZs or Sue de Coqs (when applicable). Somehow the DP-format seemed less intimidating to me, though it doesn't generally have the same eliminating power.

I understood the eliminations, but I didn't understand how the loop gives rise to the them. I have some trouble at times figuring out the eliminations from a loop, but what I look for is weak links that become strong links giving the eliminations. I didn't see 1-3 weak links in your loop, so the eliminations weren't obvious from the description.

Yeah, there are no normal weak link eliminations in that loop (because there are no 2s or 4s to eliminate by them):

(2=4)r6c6 - (4=13'2)r4c468 - loop => -13 r4c5; stte

However, we can still use bystander eliminations. Remember that ALS bystander digits (13 here) get locked in loops so we can eliminate them in all of their scopes (in this case only the row is applicable as they span two boxes) in addition to the normal weak link eliminations (none here). That's why I've pushed for a way to separate them from the linking digits and decided to use the ' as a separator. Earlier I would have written it (4=[13]2)r4c468, and I think blue used that notation some time ago in a loop as well (might actually be clearer that way, but uses two characters). In ALS loops having bystander eliminations there's no way to use the condensed notation, or any other ordering of the ALS digits, without causing more confusion, imho. In this case, however, the loop could be written differently to avoid the bystander issue (but that's not a general fix):

(1=3)r4c8 - (3=1)b5p139 - loop => -13 r4c5; stte

That way it uses just normal weak link eliminations. However, if there were any 2s or 4s to eliminate in box 5, we'd miss them with that notation, and should use the long form instead (with the bystanders preferably separated from the linking digits):

(1=3)r4c8 - (3=24'1)b5p139 - loop

It takes a second to "get" the DP description, but it works for me.

Good to know. It's not exactly intuitive at first either, but at least in this case it seems to simplify the logic once you see it. It doesn't have the same power as loops, though, as it would miss any other loop eliminations available (but here we don't have any).

Thanks for the feedback, Steve!