The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |9..|..8|17.|
 |..1|9..|.38|
 |28.|...|...|
 |---+---+---|
 |.7.|.94|...|
 |...|761|...|
 |...|83.|.4.|
 |---+---+---|
 |...|...|.85|
 |49.|..7|3..|
 |.65|2..|..4|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 9       5       36     | 346    24     8      | 1      7      26     
 67      4       1      | 9      27     56     | 256    3      8     
 2       8       367    | 136    17     356    | 4      569    69     
------------------------+----------------------+---------------------
 368     7       26     | 5      9      4      | 268    26-1   1236   
 358     23      4      | 7      6      1      | 2589  e259    239   
 56      1       9      | 8      3      2      |d56     4      7     
------------------------+----------------------+---------------------
 137     23      27     | 1346   14     369    |c679    8      5     
 4       9       8      | 16     5      7      | 3     f126    26-1   
 137     6       5      | 2      8      39     |b79    a19     4     


(1=9)r9c8* - (9=6)r79c7^ - (6=5)r6c7 - (59=2)r5c8* - (26=1)r8c8^ => -1 r4c8, r8c9; stte

Phil

PS: simpler: (6=8)r4c37 - (8=6)r4c13,r5c2 => -6 r4c89; lclste

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 9     5     36    | 346  e24    8     | 1     7     6-2   |
 | 67    4     1     | 9     7-2   56    |a256   3     8     |
 | 2     8     367   | 136   17    356   | 4     569   69    |
 *-------------------+-------------------+-------------------|
 | 368   7     26    | 5     9     4     | 268   126   1236  |
 | 358   23    4     | 7     6     1     | 2589  259   239   |
 | 56    1     9     | 8     3     2     |a56    4     7     |
 *-------------------+-------------------+-------------------|
 | 137   23    27    | 1346 d14    369   |b679   8     5     |
 | 4     9     8     |d16    5     7     | 3    c126  c126   |
 | 137   6     5     | 2     8     39    | 79    19    4     |
 *-----------------------------------------------------------*


(2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 => -2 r1c9,r2c5 ; stte

[bat999]

Code: Select all

.--------------.-----------------.--------------------.
| 9    5   36  |  346   *24  8   |  1      7    *6-2  |
| 67   4   1   |  9      27  56  | *256    3     8    |
| 2    8   367 |  136    17  356 |  4      569   69   |
:--------------+-----------------+--------------------:
| 368  7   26  |  5      9   4   |  268    126   1236 |
| 358  23  4   |  7      6   1   |  2589   259   239  |
| 56   1   9   |  8      3   2   | *56     4     7    |
:--------------+-----------------+--------------------:
| 137  23  27  |  1346  *14  369 | *679    8     5    |
| 4    9   8   | *16     5   7   |  3     *126  *126  |
| 137  6   5   |  2      8   39  | *79    *19    4    |
'--------------'-----------------'--------------------'

Contradiction if r1c9 is 2.

r1c9=2->r26c7=56->r79c7=79->r9c8=1->r8c89=26->r8c4=1->r7c5=4->r1c5=2
There's now a pair of 2's on row 1.
=> -2 r1c9 ; stte


Edit
I don't agree with Steve's solution though.
[(2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 => -2 r1c9,r2c5 ; stte]
imho it should state that there is a contradiction if r2c7<>2 (Result would be either a pair of 2's on row 1 or no 2's left in box 3).

[Leren]

Code: Select all

*---------------------------------------------------------------*
| 9     5     36     | 346   24    8      |  1     7     26     |
| 67    4     1      | 9     27    56     | c256   3     8      |
| 2     8     367    | 136   17    356    |  4     569   69     |
|--------------------+--------------------+---------------------|
| 368   7     26     | 5     9     4      | c268   126   1236   |
| 358  b23    4      | 7     6     1      | b2589 b259  b239    |
| 56    1     9      | 8     3     2      |ca56    4     7      |
|--------------------+--------------------+---------------------|
| 137   23    27     | 1346  14    369    |ca679   8     5      |
| 4     9     8      | 16    5     7      |  3     126   126    |
| 137   6     5      | 2     8     39     |ca79    1-9   4      |
*---------------------------------------------------------------*

ALS XY Wing: (9=5) r679c7 - (5=8) r5c2789 - (8=9) r24679c7 => - 9 r8c9; stte

Leren

[pjb]

bat999 wrote:

I don't agree with Steve's solution though.

Looks just fine to me.
Phil

[daj95376]

I don't agree with Steve's solution though.
[(2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 => -2 r1c9,r2c5 ; stte]
imho it should state that there is a contradiction if r2c7<>2 (Result would be either a pair of 2's on row 1 or no 2's left in box 3).

In the past, there were many formats for expressing elimination logic. When Ruud announced the AIC format, most people jumped on it as a common format. Eliminations resulted for any candidates that forced a contradiction across the endpoints of the chain.

If r1c9=2 is assumed true, then it forces the initial assumption of the chain to be true, but it conflicts with the final conclusion of the chain. Thus, the elimination -2r1c9 follows. In the past, this was expressed as:

Code: Select all

(2)r1c9 - (2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 - (2)r1c9   (assumption of true leads to conclusion of false)


Similarly,

Code: Select all

(2)r2c5 - (2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 - (2)r2c5   (assumption of true leads to conclusion of false)


However, instead of writing two discontinuous loops for the two eliminations, the AIC format used by Steve allows everything to fit in one statement.

Code: Select all

(2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 => -2 r1c9,r2c5


_

[bat999]

If r1c9=2 is assumed true, then it forces the initial assumption of the chain to be true, but it conflicts with the final conclusion of the chain. Thus, the elimination -2r1c9 follows. In the past, this was expressed as:

Code: Select all

(2)r1c9 - (2=56)r26c7 - (6)r7c7 = r8c89 - (6=14)r7c5,r8c4 - (4=2)r1c5 - (2)r1c9   (assumption of true leads to conclusion of false)


That was my solution.

Thanks for the explanation daj95376.