The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |7..|.6.|..4|
 |..8|7.4|9..|
 |.3.|...|.1.|
 |---+---+---|
 |6..|...|..5|
 |.8.|3.9|.2.|
 |...|...|...|
 |---+---+---|
 |..9|.4.|3..|
 |.2.|...|.8.|
 |...|.1.|...|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.------------------------------.----------------------.---------------------.
|  7       a(59)    b(25)      | 1289-5  6     1238-5 | 28-5   3-5    4     |
|  12-5      16-5     8        | 7       235   4      | 9      356    236   |
|e(9)24-5    3        46-25    | 2589    2589  258    | 25678  1      2678  |
:------------------------------+----------------------+---------------------:
|  6         1479   c(2)1347   | 1248    278   1278   | 1478   3479   5     |
|  145       8        1457     | 3       57    9      | 1467   2      167   |
|d(29)-1345  14579  c(2)13457  | 124568  2578  125678 | 1478   3479   13789 |
:------------------------------+----------------------+---------------------:
|  158       1567     9        | 2568    4     25678  | 3      567    1267  |
|  1345      2        134567   | 569     3579  3567   | 14567  8      1679  |
|  3458      4567     34567    | 25689   1     235678 | 24567  45679  2679  |
'------------------------------'----------------------'---------------------'


(9=5)r1c2 - (5=2)r1c3 - r36c3 = (2-9)r6c1 = (9)r3c1 - loop

=> -5 r1c4678,r2c12,r3c13; -2 r3c3; -1345 r6c1; stte

[Cenoman]

Code: Select all

 +----------------------------+---------------------------+--------------------------+
 |  7        59      25       |  12589    6      12358    | b258    f35      4       |
 |  125      156     8        |  7        235    4        |  9      f356    e236     |
 |  2459     3       2456     |  2589     2589   258      | a2578-6  1      a278-6   |
 +----------------------------+---------------------------+--------------------------+
 |  6        1479    12347    |  1248     278    1278     | c1478    3479    5       |
 |  145      8       1457     |  3        57     9        |  1467    2       167     |
 |  123459   14579   123457   |  124568   2578   125678   | c1478    3479   d13789   |
 +----------------------------+---------------------------+--------------------------+
 |  158      1567    9        |  2568     4      25678    |  3       567     1267    |
 |  1345     2       134567   |  569      3579   3567     |  14567   8       1679    |
 |  3458     4567    34567    |  25689    1      235678   |  24567   45679   2679    |
 +----------------------------+---------------------------+--------------------------+

HP(78)r3c79 = (8)r1c7 - r46c7 = (8-3)r6c9 = r2c9 - (35=6)r12c8 => -6 r3c79; ste

[SteveG48]

Code: Select all

 *------------------------------------------------------------------------------*
 | 7       9-5   ae25      | 1289-5  6       1238-5  |ae258    e35      4       |
 | 125     156     8       | 7       235     4       |  9       356    d236     |
 | 2459    3       2456    | 2589    2589    258     |  25678   1      b78      |
 *-------------------------+-------------------------+--------------------------|
 | 6       479     237     | 1248    278     1278    |  178     3479    5       |
 | 145     8       1457    | 3       57      9       |  46      2       67      |
 | 2359    4579    2357    | 12456   2578    12567   |  178     3479   c3789    |
 *-------------------------+-------------------------+--------------------------|
 | 158     1567    9       | 2568    4       25678   |  3       567     1267    |
 | 1345    2       14567   | 569     3579    3567    |  456     8       1679    |
 | 358     4567    3567    | 25689   1       235678  |  256     45679   2679    |
 *------------------------------------------------------------------------------*


(5=28)r1c37 - 8r3c9 = (8-3)r6c9 = 3r2c9 - (3=258)r1c378 => -5 r1c246 ; stte

Equivalently, we could write:

(5=238)r1c378 - (3|8)r23c9 = (38)r6c9 => -5 r1c246 ; stte

This sort of proof by contradiction generally seems to be frowned on. What do current players think?


Meanwhile, I love SpAce's loop.


Typo corrected. Thanks, Cenoman!

[Ngisa]

Code: Select all

+------------------------+--------------------------+-------------------------+
|  7      59      a25    |f12589     6      g12358  | 258     ha3-5      4    |
| b125    156      8     | 7         235     4      | 9         356      236  |
|db2459   3        2456  |e2589     e2589    258    | 25678     1        2678 |
+------------------------+--------------------------+-------------------------+
|  6      1479     12347 | 1248      278     1278   | 1478      3479     5    |
|  145    8        1457  | 3         57      9      | 1467      2        167  |
| c123459 14579    123457| 124568    2578    125678 | 1478      3479     13789|
+------------------------+--------------------------+-------------------------+
|  158    1567     9     | 2568      4       25678  | 3         567      1267 |
|  1345   2        134567| 569       3579    3567   | 14567     8        1679 |
|  3458   4567     34567 | 25689     1       235678 | 24567     45679    2679 |
+--------------------------+--------------------------+-----------------------+


(3=2)r1c38 - r23c1 = (2-9)r6c1 = r3c1 - r3c45 = (9-1)r1c4 = (1-3)r1c6 = (3)r1c8 - 5r1c8; lclste

Clement

[Ngisa]

Code: Select all

 *------------------------------------------------------------------------------*
 | 7       9-5   ae25      | 1289-5  6       1238-5  |ae258    e35      4       |
 | 125     156     8       | 7       235     4       |  9       356    d236     |
 | 2459    3       2456    | 2589    2589    258     |  25678   1      b78      |
 *-------------------------+-------------------------+--------------------------|
 | 6       479     237     | 1248    278     1278    |  178     3479    5       |
 | 145     8       1457    | 3       57      9       |  46      2       67      |
 | 2359    4579    2357    | 12456   2578    12567   |  178     3479   c3789    |
 *-------------------------+-------------------------+--------------------------|
 | 158     1567    9       | 2568    4       25678   |  3       567     1267    |
 | 1345    2       14567   | 569     3579    3567    |  456     8       1679    |
 | 358     4567    3567    | 25689   1       235678  |  256     45679   2679    |
 *------------------------------------------------------------------------------*


(5=28)r1c38 - 8r3c9 = (8-3)r6c9 = 3r2c9 - (3=258)r1c378 => -5 r1c246 ; stte

Equivalently, we could write:

(5=238)r1c378 - (3|8)r23c9 = (38)r6c9 => -5 r1c246 ; stte

This sort of proof by contradiction generally seems to be frowned on. What do current players think? I find it O.K. What is wrong?


Meanwhile, I love SpAce's loop.

[SpAce]

Equivalently, we could write:

(5=238)r1c378 - (3|8)r23c9 = (38)r6c9 => -5 r1c246 ; stte

This sort of proof by contradiction generally seems to be frowned on. What do current players think?

I'm fine with anything that's logical and understandable. However, I'd prefer to see some marker for the contradiction to make the conclusion more obvious. For example:

(5=238)r1c378 - (3|8)r23c9 = (38!)r6c9 => -5 r1c246 ; stte

or more explicitly:

(5=238)r1c378 - (3|8)r23c9 = (38!)r6c9 <-> contradiction => -5 r1c246 ; stte

or something...

Meanwhile, I love SpAce's loop.

Thanks! Your nodes could actually be turned into a loop too to get a few more eliminations (not that they're necessary). I hide it in case you want to find it yourself. (Hodoku showed me this one.)

Hidden Text: Show

Code: Select all

.-----------------------.----------------------.---------------------------.
| 7       9-5  d(25)    | 189-25  6     138-25 |d(258)   d(5)3     4       |
| 125     156    8      | 7       235   4      |  9        56-3  c(3)26    |
| 2459    3      2456   | 2589    2589  258    |  2567-8   1      a267(8)  |
:-----------------------+----------------------+---------------------------:
| 6       1479   12347  | 1248    278   1278   |  1478     3479    5       |
| 145     8      1457   | 3       57    9      |  1467     2       167     |
| 123459  14579  123457 | 124568  2578  125678 |  1478     3479  b(83)-179 |
:-----------------------+----------------------+---------------------------:
| 158     1567   9      | 2568    4     25678  |  3        567     1267    |
| 1345    2      134567 | 569     3579  3567   |  14567    8       1679    |
| 3458    4567   34567  | 25689   1     235678 |  24567    45679   2679    |
'-----------------------'----------------------'---------------------------'

(8)r3c9 = (8-3)r6c9 = r2c9 - (3=258)r1c8 - loop

=> -5 r1c246, -2 r1c46, -3 r2c8, -8 r3c7, -179 r6c9; stte

[Cenoman]

(5=28)r1c38 - 8r3c9 = (8-3)r6c9 = 3r2c9 - (3=258)r1c378 => -5 r1c246 ; stte

Equivalently, we could write:

(5=238)r1c378 - (3|8)r23c9 = (38)r6c9 => -5 r1c246 ; stte

This sort of proof by contradiction generally seems to be frowned on. What do current players think?


Meanwhile, I love SpAce's loop.

Typo: (5=28)r1c37...

No concern with the proof ! Overlapping ALSs are fully correct in chains.

I am a bit reluctant with your second writing. I would avoid including nodes that are intrinsically false into an AIC. But why not, with a marker, as suggested by SpAce ?

Note that your first writing could be simplified to:
(5=28)r1c37 - 8r3c9 = (8-3)r6c9 = 3r2c9 - (3=5)r1c8 => -5 r1c246, avoiding the ALS overlap.

[SteveG48]

Typo: (5=28)r1c37…

Thanks!

No concern with the proof ! Overlapping ALSs are fully correct in chains.

Yes, indeed. I do that all the time.

I am a bit reluctant with your second writing.

As am I, though I'm not sure why. I simply noted as I learned here that people frowned on it, and the attitude rubbed off. I suppose it may be because it has the flavor of trial and error guesswork. My point today was that even though it has that flavor, it really is the equivalent of a perfectly acceptable chain.

[eleven]

Personally i would prefer a notation, which reflects, how it was spotted - so if a contradiction was found, which leads to an elimination, it could be written that way.

However in this case i think, i would spot the strong links for 38 with the common cell r6c9 first, leading to 3r2c9=8r3c9.
Then 3r2c9 -> 5r1c8 and 8r3c9 -> 25r1c37 => -5 r1c246 (as Cenoman formulated it in the AIC above).

Very near to SpAce's solution there is an equivalent on the other side with the strong links for 29 in c1 with common cell r6c1:
2r23c1=9r3c1, 2r23c1 -> 5r1c3, 9r3c1 -> 5r1c2 => 5r1c23, stte
(and r6c1 can only be 29)

Code: Select all

 *-----------------------------------------------------------------------------------*
 |   7       a59     e25       |  12589    6      12358    |  258     35      4      |
 |  d125      156     8        |  7        235    4        |  9       356     236    |
 | db2459     3       2456     |  2589     2589   258      |  25678   1       2678   |
 |-----------------------------+---------------------------+-------------------------|
 |   6        1479    12347    |  1248     278    1278     |  1478    3479    5      |
 |   145      8       1457     |  3        57     9        |  1467    2       167    |
 |  c123459   14579   123457   |  124568   2578   125678   |  1478    3479    13789  |
 |-----------------------------+---------------------------+-------------------------|
 |   158      1567    9        |  2568     4      25678    |  3       567     1267   |
 |   1345     2       134567   |  569      3579   3567     |  14567   8       1679   |
 |   3458     4567    34567    |  25689    1      235678   |  24567   45679   2679   |
 *-----------------------------------------------------------------------------------*

(5=9)r1c2 - r3c1 = (9-2)r6c1 = r23c1 = r1c3, loop => -5r1c4678, r2c2, r3c3, -1345r6c1; stte

[SpAce]

Personally i would prefer a notation, which reflects, how it was spotted - so if a contradiction was found, which leads to an elimination, it could be written that way.

I almost agree, as it'd be instructive to know how a particular solution was actually found if it differs from the presentation. Yet there's another side of the coin. If I have to choose, I still prefer the most standard and concise presentation instead of someone's raw stream of consciousness (which I might not bother to decipher). In fact, I think writing that is another fun and instructive step of the solving process, especially if it involves transforming the initial solution to a more standard/elegant form (eg. forcing chain -> AIC, net -> ALS / split-nodes; contradiction -> verity, etc). However, it wouldn't hurt to show both, especially if the spotting process was particularly clever and different from the preferred presentation.