The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|5.8|.29|
 |..2|.9.|17.|
 |9..|..7|...|
 |---+---+---|
 |.3.|9..|..5|
 |...|...|...|
 |6..|..3|.8.|
 |---+---+---|
 |...|4..|..8|
 |.25|.3.|7..|
 |31.|8.6|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 14      7       3        | 5       16      8        | 46      2       9        |
| 5       8       2        | 36      9       4        | 1       7       36       |
| 9       46     a16       |c23     b12      7        | 8       5       34       |
|--------------------------+--------------------------+--------------------------|
| 124     3       7        | 9       8       12       | 246     46      5        |
| 124     459     8        | 267     2456    125      | 249     3       17       |
| 6       459     9-1      |d27      245     3        | 249     8      e17       |
|--------------------------+--------------------------+--------------------------|
| 7       69      69       | 4       25      25       | 3       1       8        |
| 8       2       5        | 1       3       9        | 7       46      46       |
| 3       1       4        | 8       7       6        | 5       9       2        |
*--------------------------------------------------------------------------------*

(1) r3c3 = (1-2) r3c5 = r3c4 - (2=7) r6c4 - (7=1) r6c9 => r6c3 <> 1; stte

Leren

[ArkieTech]

Same result

Code: Select all

 *-----------------------------------------------------------*
 | 14    7     3     | 5     16    8     | 46    2     9     |
 | 5     8     2     | 36    9     4     | 1     7     36    |
 | 9    a46   a16    |b23    12    7     | 8     5    b34    |
 |-------------------+-------------------+-------------------|
 | 124   3     7     | 9     8     12    | 246   46    5     |
 | 124   459   8     | 267   2456  125   | 249   3     17    |
 | 6     459   9-1   |c27    245   3     | 249   8    c17    |
 |-------------------+-------------------+-------------------|
 | 7     69    69    | 4     25    25    | 3     1     8     |
 | 8     2     5     | 1     3     9     | 7     46    46    |
 | 3     1     4     | 8     7     6     | 5     9     2     |
 *-----------------------------------------------------------*
 als xy-wing (3 sets)
(1=4)r3c23-(4=2)r3c49-(2=1)r6c49 => -1r6c3; stte

[tlanglet]

Almost Sue de Coq (124567)r5c456, (127)r4c6&r6c4, (45=9)r5c2

9r5c2-(9=1*=7=2)r6c394-r3c4=(2-1)r3c5=1r3c3 Conflict => r5c2<>9
Thus, Sdc is true => r5c17<>4, r6c5<>2

Fun ASdC but coloring 4 is needed to complete the puzzle.

Ted

[tlanglet]

Numerous deletions result from an
ANS(27=6)r65c4-r5c5=(6-1)r1c5=r1c1-r3c3=(1=7=2)r6c394 => r3c4, r56c5,r45c6<>2

[storm_norm22]

another one

Code: Select all

+----------------+-----------------+----------------+
| 14   7    3    | 5     16    8   | 46   2   9     |
| 5    8    2    | 36    9     4   | 1    7   36    |
| 9    46   6(1) | 3(2)  (12)  7   | 8    5   34    |
+----------------+-----------------+----------------+
| 124  3    7    | 9     8     12  | 246  46  5     |
| 124  459  8    | 26-7  2456  125 | 249  3   (17)  |
| 6    459  9(1) | (27)  245   3   | 249  8   -7(1) |
+----------------+-----------------+----------------+
| 7    69   69   | 4     25    25  | 3    1   8     |
| 8    2    5    | 1     3     9   | 7    46  46    |
| 3    1    4    | 8     7     6   | 5    9   2     |
+----------------+-----------------+----------------+

(1=7)r5c9 - (1)r6c9 = (1)r6c3 - (1)r3c3 = (1-2)r3c5 = (2)r3c4 - (2=7)r6c4; r5c4 and r6c9 <> 7

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 14      7       3        | 5       16      8        | 46      2       9        |
| 5       8       2        | 36      9       4        | 1       7       36       |
| 9      a46A    a16A      |a23A     12      7        | 8       5      a34A      |
|--------------------------+--------------------------+--------------------------|
| 124     3       7        | 9       8       12       | 246     46      5        |
| 124     459     8        | 267     2456    125      | 249     3       17       |
| 6      c459B   b19B      | 7-2    c245B    3        |c249B    8       17       |
|--------------------------+--------------------------+--------------------------|
| 7       69      69       | 4       25      25       | 3       1       8        |
| 8       2       5        | 1       3       9        | 7       46      46       |
| 3       1       4        | 8       7       6        | 5       9       2        |
*--------------------------------------------------------------------------------*

For als xy-wing fans here's another one with a different elimination (small letters) :

(2=1) r2c2349 - (1=9) r6c3 - (9=2) r6c257 => r6c4 <> 2; stte

The same result also comes from the als xz-rule (capital letters):

(2=1) r3c2349 - (1=2) r6c2357=> r6c4 <> 2; stte

Leren

[Marty R.]

Code: Select all

+------------+--------------+-----------+
| 14  7   3  | 5   16   8   | 46  2  9  |
| 5   8   2  | 36  9    4   | 1   7  36 |
| 9   46  16 | 23  12   7   | 8   5  34 |
+------------+--------------+-----------+
| 124 3   7  | 9   8    12  | 246 46 5  |
| 124 459 8  | 267 2456 125 | 249 3  17 |
| 6   459 19 | 27  245  3   | 249 8  17 |
+------------+--------------+-----------+
| 7   69  69 | 4   25   25  | 3   1  8  |
| 8   2   5  | 1   3    9   | 7   46 46 |
| 3   1   4  | 8   7    6   | 5   9  2  |
+------------+--------------+-----------+


Play this puzzle online at the Daily Sudoku site

Basically same as leren, but longer path.

(1=6)r3c3-(6=4)r3c2-(4=3)r3c9-(3=2)r3c4-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

I continue to have problems grasping ALS's and wonder if this shortened notation is valid:

(1=6)r3c3-(6=1342)r3c2594-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

[DonM]

Code: Select all

+------------+--------------+-----------+
| 14  7   3  | 5   16   8   | 46  2  9  |
| 5   8   2  | 36  9    4   | 1   7  36 |
| 9   46  16 | 23  12   7   | 8   5  34 |
+------------+--------------+-----------+
| 124 3   7  | 9   8    12  | 246 46 5  |
| 124 459 8  | 267 2456 125 | 249 3  17 |
| 6   459 19 | 27  245  3   | 249 8  17 |
+------------+--------------+-----------+
| 7   69  69 | 4   25   25  | 3   1  8  |
| 8   2   5  | 1   3    9   | 7   46 46 |
| 3   1   4  | 8   7    6   | 5   9  2  |
+------------+--------------+-----------+


Play this puzzle online at the Daily Sudoku site

Basically same as leren, but longer path.

(1=6)r3c3-(6=4)r3c2-(4=3)r3c9-(3=2)r3c4-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

I continue to have problems grasping ALS's and wonder if this shortened notation is valid:

(1=6)r3c3-(6=1342)r3c2594-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

You're very close and the ALS notation is accurate. However, all the 2s in your ALS have to see the target digit of your ALS, in this case (2)r6c4). You have two 2s in the ALS: (2)r3c4 and (2)r3c5, but the target digit, (2)r6c4, only sees (2)r3c4, not (2)r3c4 so the chain is not going to work.

However, you can make it work by simply shortening the ALS by eliminating (12)r3c5 from it:
(1=6)r3c3-(6=234)r3c249-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

Now the only 2 in the ALS sees (2)r6c4 and all is well.

[eleven]

As Leren demonstrated, you can write it as als xz as well:
als xz: (1=2346)r3c2349-(2=17)r6c49 => r4c3<>1

[Marty R.]

Code: Select all

+------------+--------------+-----------+
| 14  7   3  | 5   16   8   | 46  2  9  |
| 5   8   2  | 36  9    4   | 1   7  36 |
| 9   46  16 | 23  12   7   | 8   5  34 |
+------------+--------------+-----------+
| 124 3   7  | 9   8    12  | 246 46 5  |
| 124 459 8  | 267 2456 125 | 249 3  17 |
| 6   459 19 | 27  245  3   | 249 8  17 |
+------------+--------------+-----------+
| 7   69  69 | 4   25   25  | 3   1  8  |
| 8   2   5  | 1   3    9   | 7   46 46 |
| 3   1   4  | 8   7    6   | 5   9  2  |
+------------+--------------+-----------+


Play this puzzle online at the Daily Sudoku site

Basically same as leren, but longer path.

(1=6)r3c3-(6=4)r3c2-(4=3)r3c9-(3=2)r3c4-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

I continue to have problems grasping ALS's and wonder if this shortened notation is valid:

(1=6)r3c3-(6=1342)r3c2594-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

You're very close and the ALS notation is accurate. However, all the 2s in your ALS have to see the target digit of your ALS, in this case (2)r6c4). You have two 2s in the ALS: (2)r3c4 and (2)r3c5, but the target digit, (2)r6c4, only sees (2)r3c4, not (2)r3c4 so the chain is not going to work.

However, you can make it work by simply shortening the ALS by eliminating (12)r3c5 from it:
(1=6)r3c3-(6=234)r3c249-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

Now the only 2 in the ALS sees (2)r6c4 and all is well.

Don,

Thank you, I always welcome critique. I understand how my ALS was bloated and included unnecessary cells.

I don't understand the concept of all the 2s having to see the target digit. I thought the last digit of one term had to be the beginning digit of the next. So the 2 was established in r3c4 and the term in r6c4 started with 2. I'm not understanding why all 2s need to see the target.

[DonM]

Code: Select all

+------------+--------------+-----------+
| 14  7   3  | 5   16   8   | 46  2  9  |
| 5   8   2  | 36  9    4   | 1   7  36 |
| 9   46  16 | 23  12   7   | 8   5  34 |
+------------+--------------+-----------+
| 124 3   7  | 9   8    12  | 246 46 5  |
| 124 459 8  | 267 2456 125 | 249 3  17 |
| 6   459 19 | 27  245  3   | 249 8  17 |
+------------+--------------+-----------+
| 7   69  69 | 4   25   25  | 3   1  8  |
| 8   2   5  | 1   3    9   | 7   46 46 |
| 3   1   4  | 8   7    6   | 5   9  2  |
+------------+--------------+-----------+


Play this puzzle online at the Daily Sudoku site

Basically same as leren, but longer path.

(1=6)r3c3-(6=4)r3c2-(4=3)r3c9-(3=2)r3c4-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

I continue to have problems grasping ALS's and wonder if this shortened notation is valid:

(1=6)r3c3-(6=1342)r3c2594-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

You're very close and the ALS notation is accurate. However, all the 2s in your ALS have to see the target digit of your ALS, in this case (2)r6c4). You have two 2s in the ALS: (2)r3c4 and (2)r3c5, but the target digit, (2)r6c4, only sees (2)r3c4, not (2)r3c4 so the chain is not going to work.

However, you can make it work by simply shortening the ALS by eliminating (12)r3c5 from it:
(1=6)r3c3-(6=234)r3c249-(2=7)r6c4-(7=1)r6c9=>r6c3<>1

Now the only 2 in the ALS sees (2)r6c4 and all is well.

Don,

Thank you, I always welcome critique. I understand how my ALS was bloated and included unnecessary cells.

I don't understand the concept of all the 2s having to see the target digit. I thought the last digit of one term had to be the beginning digit of the next. So the 2 was established in r3c4 and the term in r6c4 started with 2. I'm not understanding why all 2s need to see the target.

The answer lies in what is the basis for the target being a target. In the revised/simpler ALS above, if the ALS becomes a locked set then the digits 2,3,4 will be locked in cells r3c249. Since there is only one 2, it has to be locked in r3c4 so then, simplistically, the target digit (2)r6c4, would be removed or logically be in a 'not state'.

However, if this were the original ALS and the set becomes locked then you have the digits 1,2,3,4 locked in cells r3c2459, but now there are two 2s, one in r3c4 and one in r3c5. This is where things can seem a little tricky: One can look at the digits in this particular locked set and figure out which digits would end up in each cell, but the chain doesn't establish that so until proven otherwise, the 2 could end up in r3c4 or r3c5; thus, one can't assume that it will end up as the sole digit in r3c4 which would be the basis for its effect on target digit (2)r6c4.

btw: Note that if the target digit was in r3, there would be no problem since even if there were two 2s in the locked set in r3, one of them would have to end up as a solved 2 for a cell in r3, thus driving the target digit (again, assuming it is in r3) into a not state.

Hope that helps.

[Marty R.]

Hope that helps.

Thanks Don, I think it's starting to sink in.