The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|..3|
 |...|1.3|7..|
 |...|...|984|
 |---+---+---|
 |5..|8.1|.3.|
 |9..|5.7|..1|
 |.3.|6.4|..2|
 |---+---+---|
 |412|...|...|
 |..9|2.5|...|
 |6..|...|...|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 278     45678   45678  |a49     4568   689    | 126    1256   3     
 28      9       4568   | 1      4568   3      | 7      256    56     
 13      56      13     | 7      56     2      | 9      8      4     
------------------------+----------------------+---------------------
 5       467     467    | 8      2      1      | 46     3      9     
 9       2       46     | 5      3      7      | 8      46     1     
 18      3       18     | 6      9      4      | 5      7      2     
------------------------+----------------------+---------------------
 4       1       2      | 3-9    678    689    | 36     569    5678   
 378     78      9      | 2      14678  5      | 1346   146    678   
 6      b578    b3578   |b349    1478  b89     | 1234   1249  b78     


(9=4)r1c4 - (4=9)r9c23469 => -9 r7c4; stte

Phil

[SpAce]

An ugly variant of Phil's:

Code: Select all

.--------------------.--------------------.-------------------.
| 278   45678  45678 |a49   4568      689 | 126   1256   3    |
| 28    9      4568  | 1    4568      3   | 7     256    56   |
| 13    56     13    | 7    56        2   | 9     8      4    |
:--------------------+--------------------+-------------------:
| 5     467    467   | 8    2         1   | 46    3      9    |
| 9     2      46    | 5    3         7   | 8     46     1    |
| 18    3      18    | 6    9         4   | 5     7      2    |
:--------------------+--------------------+-------------------:
| 4     1      2     | 3-9  678       689 | 36    569    5678 |
| 378   78     9     | 2    14678     5   | 1346  146    678  |
| 6    b578  *(3578) |a349  1478   dcb89  | 1234  1249 cb78   |
'--------------------'--------------------'-------------------'

Death Blossom (3578)r9c3

(3) - (3=49)r19c4
||
(5) - (5=789)r9c296
||
(7) - (7=89)r9c96
||
(8) - (8=9)r9c6

=> -9 r7c4; stte

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 | 278    45678  45678  | 49     4568   689    |  126    1256   3      |
 | 28     9      4568   | 1      4568   3      |  7      256    6-5    |
 | 13     56     13     | 7      56     2      |  9      8      4      |
 *----------------------+----------------------+-----------------------|
 | 5      467    467    | 8      2      1      |  46     3      9      |
 | 9      2      46     | 5      3      7      |  8      46     1      |
 | 18     3      18     | 6      9      4      |  5      7      2      |
 *----------------------+----------------------+-----------------------|
 | 4      1      2      |b39    b678   b689    |ad36     69-5 ad5678   |
 | 378    78     9      | 2     c14678  5      | d1346  d146  ad678    |
 | 6      578    3578   | 349    1478  b89     |  1234   1249 ad78     |
 *---------------------------------------------------------------------*


Can't beat Phil's, so:

(5=3678)b9p1369 - (3=6789)b8p1239 - (6|7|8=1|4)r8c5 - (134678=5)b9p134569 => -5 r2c9,r7c8 ; stte

[Ngisa]

Code: Select all

+-------------------------+-----------------------+------------------------+
| 278     45678     45678 | 49      4568      689 | 126      1256     3    |
| 28      9         4568  | 1       4568      3   | 7        256      56   |
| 13      56        13    | 7       56        2   | 9        8        4    |
+-------------------------+-----------------------+------------------------+
| 5       467       467   | 8       2         1   | 46       3        9    |
| 9       2         46    | 5       3         7   | 8        46       1    |
| 18      3         18    | 6       9         4   | 5        7        2    |
+-------------------------+-----------------------+------------------------+
| 4       1         2     | d39     678       689 | c36      569      5678 |
|a378    a78        9     | 2       14678     5   | 1346     146     b678  |
| 6       578       578-3 |e349     1478      89  | 1234     1249     78   |
+-------------------------+-----------------------+------------------------+


(3=78)r8c12 - (78=6)r8c9 - (6=3)r7c7 - r7c4 = r9c4 => - 3r9c3; lclste

Clement

[SpAce]

(3=78)r8c12 - (78=6)r8c9 - (6=3)r7c7 - r7c4 = (3)r9c4 => - 3r9c3; lclste

Again, the first weak link is technically incorrect (by Eureka rules) for the same reason the last one was. Should be ... - (7|8=6)r8c9 - ... Believe it or not! (I'm not trying to be annoying, even though I probably am -- just trying to help with something that used to be unintuitive for me too.)

Edit: Just to clarify, there's nothing wrong with the first weak link per se, but the next node pair (78=6)r8c9 after that.

[Ngisa]

(3=78)r8c12 - (78=6)r8c9 - (6=3)r7c7 - r7c4 = (3)r9c4 => - 3r9c3; lclste

Again, the first weak link is technically incorrect (by Eureka rules) for the same reason the last one was. Should be ... - (7|8=6)r8c9 - ... Believe it or not! (I'm not trying to be annoying, even though I probably am -- just trying to help with something that used to be unintuitive for me too.)

If r8c1 is not 3, you have a naked pair 78 in r8c12, what is wrong when you say (3=78)r8c12?

[SpAce]

(3=78)r8c12 - (78=6)r8c9 - (6=3)r7c7 - r7c4 = (3)r9c4 => - 3r9c3; lclste

Again, the first weak link is technically incorrect (by Eureka rules) for the same reason the last one was. Should be ... - (7|8=6)r8c9 - ... Believe it or not! (I'm not trying to be annoying, even though I probably am -- just trying to help with something that used to be unintuitive for me too.)

If r8c1 is not 3, you have a naked pair 78 in r8c12, what is wrong when you say (3=78)r8c12?

Nothing. Was that the part I said was incorrect? Nope (though I admit I communicated unclearly). It's the next node. I already tried to explain this yesterday, but I guess I didn't do a very good job. I'll give it one more shot.

The problem becomes clearer if your chain is reversed (I presume you know that AICs are supposed to be bidirectional):

(3)r9c4 = r7c4 - (3=6)r7c7 - (6=78)r8c9 - (78=3)r8c12

Like I said, a group of digits has implied ANDs ("&") between them unless otherwise specified, so it's just a shorthand for this:

(3)r9c4 = r7c4 - (3=6)r7c7 - (6=7&8)r8c9 - (7&8=3)r8c12

Does that chain make sense to you? It shouldn't. The strong link (6=7&8)r8c9 is illogical, because it says: "if r8c9 <> 6, then r8c9 = (7 AND 8)". A single cell can't hold two values, so that's clearly wrong. It should say: "if r8c9 <> 6, then r8c9 = (7 OR 8)", which allows the chain to continue (because either value 7 or 8 makes the next link work). So, the correct way to write is:

(3)r9c4 = r7c4 - (3=6)r7c7 - (6=7|8)r8c9 - (7&8=3)r8c12

Or more typically without the "&" because it's implied:

(3)r9c4 = r7c4 - (3=6)r7c7 - (6=7|8)r8c9 - (78=3)r8c12

That can be read correctly either way, so in the original direction it's:

(3=78)r8c12 - (7|8=6)r8c9 - (6=3)r7c7 - r7c4 = (3)r9c4

In that direction the interpretation is: "if r8c12 = (7 AND 8), then r8c9 <> (7 OR 8)" which is the same as "if r8c12 = (7 AND 8), then (r8c9 <> 7 AND r8c9 <> 8)". That leaves 6 as the only value in r8c9, so the chain can continue.

If there's an (implied) AND instead of an explicit OR, as in your original chain, the interpretation is: "if r8c12 = (7 AND 8), then r8c9 <> (7 AND 8)" which is the same as ""if r8c12 = (7 AND 8), then (r8c9 <> 7 OR r8c9 <> 8)", which does not leave 6 as the only possibility in that cell and the chain can't continue.

Added: PS. I hadn't realized that you've been an active member for many years. I understand if my comments aren't appreciated with that background. Doesn't mean I'm wrong, though, but I guess I should sometimes just shut up

[eleven]

Code: Select all

 *-----------------------------------------------------------------------*
 |  278   45678   45678   |  49    4568    689   |  126    1256   3      |
 |  28    9       4568    |  1     4568    3     |  7      256    56     |
 |  13    56      13      |  7     56      2     |  9      8      4      |
 |------------------------+----------------------+-----------------------|
 |  5     467     467     |  8     2       1     |  46     3      9      |
 |  9     2       46      |  5     3       7     |  8      46     1      |
 |  18    3       18      |  6     9       4     |  5      7      2      |
 |------------------------+----------------------+-----------------------|
 |  4     1       2       | a39    678     689   |  36     569    5678   |
 |  378   78      9       |  2     14678   5     |  1346   146    678    |
 |  6    b578    b3578    |  49-3  1478   b89    |  1234   1249  b78     |
 *-----------------------------------------------------------------------*

(3=9)r7c4 - (9=8753)r9c2369 => -3r9c4; stte

[rjamil]

Code: Select all

........3...1.37........9845..8.1.3.9..5.7..1.3.6.4..2412........92.5...6........
 +-------------------+---------------+------------------+
 | 278   45678 45678 | 49  4568  689 | 126   1256 3     |
 | 28    9     4568  | 1   4568  3   | 7     256  56    |
 | 13    56    13    | 7   56    2   | 9     8    4     |
 +-------------------+---------------+------------------+
 | 5     467   467   | 8   2     1   | 46    3    9     |
 | 9     2     46    | 5   3     7   | 8     46   1     |
 | 18    3     18    | 6   9     4   | 5     7    2     |
 +-------------------+---------------+------------------+
 | 4     1     2     | 39  678   689 | (36)  569  5678  |
 | (378) (78)  9     | 2   14678 5   | 146-3 146  (678) |
 | 6     578   3578  | 349 1478  89  | 1234  1249 78    |
 +-------------------+---------------+------------------+

WXYZ-Wings: 3678 @ Apex r8c9, Wings Box r7c7, Row r8c12 => -3 r8c7; lclste

R. Jamil