The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|..8|...|
 |..9|...|...|
 |52.|.4.|3..|
 |---+---+---|
 |..5|.6.|..7|
 |976|5.2|1..|
 |1..|...|..9|
 |---+---+---|
 |..7|..5|...|
 |2..|.93|..4|
 |31.|...|6..|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
|c47     b46      3        |c127    c257     8        | 9      c257     126      |
| 78      8-6     9        | 1237    2357   a16       | 4       257     126      |
| 5       2       1        | 79      4       69       | 3       78      68       |
|--------------------------+--------------------------+--------------------------|
| 48      348     5        | 19      6       19       | 28      238     7        |
| 9       7       6        | 5       38      2        | 1       4       38       |
| 1       38      2        | 378     378     4        | 5       6       9        |
|--------------------------+--------------------------+--------------------------|
| 6       9       7        | 4       1       5        | 28      238     238      |
| 2       5       8        | 6       9       3        | 7       1       4        |
| 3       1       4        | 28      28      7        | 6       9       5        |
*--------------------------------------------------------------------------------*

ANS XY Wing: (6=1) r2c6 -1r1c4 = 4r1c1 [ANS(12457)r1c1458] - (4=6) r1c2 => r2c2 <6> ; stte

Leren

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 47     d46      3        |b127     257     8        | 9       257    c126      |
| 78      8-6     9        | 1237    2357   a16       | 4       257     126      |
| 5       2       1        | 79      4       69       | 3       78      68       |
|--------------------------+--------------------------+--------------------------|
| 48      348     5        | 19      6       19       | 28      238     7        |
| 9       7       6        | 5       38      2        | 1       4       38       |
| 1       38      2        | 378     378     4        | 5       6       9        |
|--------------------------+--------------------------+--------------------------|
| 6       9       7        | 4       1       5        | 28      238     238      |
| 2       5       8        | 6       9       3        | 7       1       4        |
| 3       1       4        | 28      28      7        | 6       9       5        |
*--------------------------------------------------------------------------------*

M Wing: (6=1) r1c6 - r1c4 = (1-6) r1c9 = 6r1c2 => r2c2 <6>; stte

Leren

[pjb]

How about:

(6)r1c2 = (6-1)r1c9 = (1)r1c4 - (1-6)r2c6: => r2c2 <> 6; stte

Season's Greetings, Phil

[ArkieTech]

Code: Select all

 *-----------------------------------------------------------*
 | 47   a46    3     | 127   257   8     | 9     257  e12-6  |
 | 78   b68    9     | 1237  2357 c16    | 4     257  d126   |
 | 5     2     1     | 79    4     69    | 3     78    68    |
 |-------------------+-------------------+-------------------|
 | 48    348   5     | 19    6     19    | 28    238   7     |
 | 9     7     6     | 5     38    2     | 1     4     38    |
 | 1     38    2     | 378   378   4     | 5     6     9     |
 |-------------------+-------------------+-------------------|
 | 6     9     7     | 4     1     5     | 28    238   238   |
 | 2     5     8     | 6     9     3     | 7     1     4     |
 | 3     1     4     | 28    28    7     | 6     9     5     |
 *-----------------------------------------------------------*
s-wing
6r1c2=r2c2-(6=1)r2c6-r2c9=1r1c9 => -6r1c9; stte

[storm_norm22]

found some other paths, but that m-wing does the trick

[daj95376]

found some other paths, but that m-wing does the trick

Is this one of the other paths you found?

Code: Select all

 after basics
 +--------------------------------------------------------------+
 |  47   c46    3     |  127   257   8     |  9     257  d126   |
 | h78   g68    9     |  1237  2357 f16    |  4     257  e126   |
 |  5     2     1     |  79    4     69    |  3     78    68    |
 |--------------------+--------------------+--------------------|
 | i48   b348   5     |  19    6     19    | j28   a238j  7     |
 |  9     7     6     |  5     38    2     |  1     4     38    |
 |  1     38    2     |  378   378   4     |  5     6     9     |
 |--------------------+--------------------+--------------------|
 |  6     9     7     |  4     1     5     |  28    238   238   |
 |  2     5     8     |  6     9     3     |  7     1     4     |
 |  3     1     4     |  28    28    7     |  6     9     5     |
 +--------------------------------------------------------------+
 # 49 eliminations remain

 (3)r4c8 = (3-4)r4c2 = (4-6)r1c2 = (6-1)r1c9 = r2c9 -
 (1=6)r2c6 - (6=8)r2c2 - r2c1 = r4c1 - (28=3)r4c78  =>  r4c8<>28


[Marty R.]

Code: Select all

+----------+--------------+------------+
| 47 46  3 | 127  257  8  | 9  257 126 |
| 78 68  9 | 1237 2357 16 | 4  257 126 |
| 5  2   1 | 79   4    69 | 3  78  68  |
+----------+--------------+------------+
| 48 348 5 | 19   6    19 | 28 238 7   |
| 9  7   6 | 5    38   2  | 1  4   38  |
| 1  38  2 | 378  378  4  | 5  6   9   |
+----------+--------------+------------+
| 6  9   7 | 4    1    5  | 28 238 238 |
| 2  5   8 | 6    9    3  | 7  1   4   |
| 3  1   4 | 28   28   7  | 6  9   5   |
+----------+--------------+------------+


Play this puzzle online at the Daily Sudoku site

I tried this chain and, as is often the case, don't know if the notation is valid.

(8=4)r4c1-(4=7)r1c1-(12457=6)r1c45892-(6=8)r2c2=>r2c1<>8

A longer version:

(8=4)r4c1-(4=7)r1c1-(257=1)r1c584-(1=6)r2c6-(6=8)r2c2=>r2c1<>8

[DonM]

Code: Select all

+----------+--------------+------------+
| 47 46  3 | 127  257  8  | 9  257 126 |
| 78 68  9 | 1237 2357 16 | 4  257 126 |
| 5  2   1 | 79   4    69 | 3  78  68  |
+----------+--------------+------------+
| 48 348 5 | 19   6    19 | 28 238 7   |
| 9  7   6 | 5    38   2  | 1  4   38  |
| 1  38  2 | 378  378  4  | 5  6   9   |
+----------+--------------+------------+
| 6  9   7 | 4    1    5  | 28 238 238 |
| 2  5   8 | 6    9    3  | 7  1   4   |
| 3  1   4 | 28   28   7  | 6  9   5   |
+----------+--------------+------------+


I tried this chain and, as is often the case, don't know if the notation is valid.

(8=4)r4c1-(4=7)r1c1-(12457=6)r1c45892-(6=8)r2c2=>r2c1<>8

When notating an ALS, it's best to have the notation reflect the actual left-to-right 'logic stream' in the chain:
Thus: (8=4)r4c1-(4=7)r1c1-(7=12456)r1c24589-(6=8)r2c2 etc.

The logic stream in the underlined portion as notated now reads:
(in r1c1) if not 4 then 7 -> not 7 in r1c24589 thus locking the remaining 12456 in r1c24589 resulting in: not 6 in r2c2 etc.

(I prefer using the label 'als' but left it out here so as to not confuse the issue.)

[ronk]

Code: Select all

+----------+--------------+------------+
| 47 46  3 | 127  257  8  | 9  257 126 |
| 78 68  9 | 1237 2357 16 | 4  257 126 |
| 5  2   1 | 79   4    69 | 3  78  68  |
+----------+--------------+------------+
| 48 348 5 | 19   6    19 | 28 238 7   |
| 9  7   6 | 5    38   2  | 1  4   38  |
| 1  38  2 | 378  378  4  | 5  6   9   |
+----------+--------------+------------+
| 6  9   7 | 4    1    5  | 28 238 238 |
| 2  5   8 | 6    9    3  | 7  1   4   |
| 3  1   4 | 28   28   7  | 6  9   5   |
+----------+--------------+------------+


I tried this chain and, as is often the case, don't know if the notation is valid.

(8=4)r4c1-(4=7)r1c1-(12457=6)r1c45892-(6=8)r2c2=>r2c1<>8

The 6s in r1c9 and r2c2 do not see each other. Were r1c9<>2 done with a prior move, the puzzle would already be reduced to a cascade of singles.

[Marty R.]

Thanks Don and Ron.

The 6s in r1c9 and r2c2 do not see each other. Were r1c9<>2 done with a prior move, the puzzle would already be reduced to a cascade of singles.

Ron, I don't understand. What's the significance of the two 6s not seeing each other?

[DonM]

Thanks Don and Ron.

The 6s in r1c9 and r2c2 do not see each other. Were r1c9<>2 done with a prior move, the puzzle would already be reduced to a cascade of singles.

Ron, I don't understand. What's the significance of the two 6s not seeing each other?

I'll answer that since I feel remiss in not having checked the logic of the ALS before discussing the notation of it. Ron is right. The general rule is that when you are assuming that a given target digit downstream of the ALS would be 'not' if the locked set were to occur then all digits in that locked set that are the same as the target digit must 'see' that target digit.

The practical reason is that if you look at your ALS, there are 2 6s in what would be the resulting locked set, one at r1c2 and one at r1c9. Your chain assumes that the locked set that would occur if 'not 7' occurred would knock out the 6 in r2c2, but you don't know that because the locked set (until proven otherwise) could consist of a 4 in r1c2 and a 6 in r1c9. Only if both 6s in your ALS (at r1c2 and r1c9) were to 'see' the 6 in r2c2 could you be sure that it would be 'not 6' as your chain assumes.

Fwiw: this is one of the easiest mistakes to make in a longer ALS structure.