The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.1.|...|.8.|
 |9..|...|7.3|
 |5..|8..|96.|
 |---+---+---|
 |...|62.|3..|
 |76.|3.1|.25|
 |..2|.45|...|
 |---+---+---|
 |.54|..7|..6|
 |6.1|...|..9|
 |.9.|...|.7.|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
|b34      1       367      | 49-5    3679-5 c346      |a25      8      a24       |
| 9       248     68       |c1245   c156    c246      | 7       4-5     3        |
| 5       24      37       | 8       37     c24       | 9       6       1        |
|--------------------------+--------------------------+--------------------------|
| 48      48      5        | 6       2       9        | 3       1       7        |
| 7       6       9        | 3       8       1        | 4       2       5        |
| 1       3       2        | 7       4       5        | 6       9       8        |
|--------------------------+--------------------------+--------------------------|
| 28      5       4        | 129     19      7        | 128     3       6        |
| 6       7       1        | 245     35      2348     | 258     45      9        |
| 238     9       38       | 1245    156     2468     | 1258    7       24       |
*--------------------------------------------------------------------------------*

als xy-wing: (5=4) r1c79 - (4=3) r1c1 - (3=5) r2c45, r123c6 => r1c45, r2c8 <> 5; stte

Leren

[pjb]

Here's an XY chain which does the trick:

(2=8)r7c1 - 8 - (8=3) r9c3 - 3 - (3=7) r3c3 - 7 - (7=3)r3c5 - 3 - (3=5)r8c5 - 5 - (5=4)r8c8 - 4 - (4=2)r9c9: => -2r9c1, r7c7, stte.

Phil

[SudoQ]

Here is one, followed by a pair:

Code: Select all

|---------------|-------------------|--------------|
| 34   1    367 | 459   35679 (3)4-6| 25    8   24 |
| 9    248 (68) | 1245  15(6)  24(6)| 7     45  3  |
| 5    24   37  | 8     37     24   | 9     6   1  |
|---------------|-------------------|--------------|
| 48   48   5   | 6     2      9    | 3     1   7  |
| 7    6    9   | 3     8      1    | 4     2   5  |
| 1    3    2   | 7     4      5    | 6     9   8  |
|---------------|-------------------|--------------|
| 28   5    4   | 129   19     7    | 128   3   6  |
| 6    7    1   | 245   35    24(38)| 258   45  9  |
| 238  9   3(8) | 1245  156   246(8)| 1258  7   24 |
|---------------|-------------------|--------------|

/SudoQ

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 34      1       367      | 459     5679-3 c346      | 25      8       24       |
| 9       248     68       |c1245   c156    c246      | 7      b45      3        |
| 5       24      37       | 8       7-3    c24       | 9       6       1        |
|--------------------------+--------------------------+--------------------------|
| 48      48      5        | 6       2       9        | 3       1       7        |
| 7       6       9        | 3       8       1        | 4       2       5        |
| 1       3       2        | 7       4       5        | 6       9       8        |
|--------------------------+--------------------------+--------------------------|
| 28      5       4        | 129     19      7        | 128     3       6        |
| 6       7       1        | 245    a35      248-3    | 258    a45      9        |
| 238     9       38       | 1245    156     2468     | 1258    7       24       |
*--------------------------------------------------------------------------------*

Another als xy-wing: (3=4) r8c58 - (4=5) r2c8 - (5=3) r2c45, r123c6 => r13c5, r8c6 <> 3; stte

Leren

[eleven]

SudoQ, this elimination can also be done with
als xz-wing: (6=8r139c3)-(8=6r239c6)=>r1c6<>6
(either r1c3=6 or r13c3=37->r9c3=8->r289c6=246)

[tlanglet]

Why solve an usually non-extreme puzzle with a non-extreme solution. Here is one that is at least longer and messier......

Type 4 UR(37)r13c35 => r1c35<>3 which is not very useful. However, looking at the internal SIS we find: 6r1c3 & 569r1c5

6r1c3-ALS(2346)r1c169[6r1c6=2r1c9]-(2=4)r9c9-(4=5)r8c8 => r8c5<>5
569r1c5: quantum naked quad (1569)r1279 => r8c5<>5
Thus, r8c5<>5 to complete the puzzle

Ted

Editorial Note: Given the recent discussion on pseudocells, I decided to use the term "quantum" for the first time. No idea if it is proper in this circumstance.

[Marty R.]

Code: Select all

+-------------+-----------------+------------+
| 34  1   367 | 459  35679 346  | 25   8  24 |
| 9   248 68  | 1245 156   246  | 7    45 3  |
| 5   24  37  | 8    37    24   | 9    6  1  |
+-------------+-----------------+------------+
| 48  48  5   | 6    2     9    | 3    1  7  |
| 7   6   9   | 3    8     1    | 4    2  5  |
| 1   3   2   | 7    4     5    | 6    9  8  |
+-------------+-----------------+------------+
| 28  5   4   | 129  19    7    | 128  3  6  |
| 6   7   1   | 245  35    2348 | 258  45 9  |
| 238 9   38  | 1245 156   2468 | 1258 7  24 |
+-------------+-----------------+------------+


Play this puzzle online at the Daily Sudoku site

I used the Type 3 UR in band 1, 24-24-248-246. The 8 proves a 6 in r9c6=>r1c6<>1. My path wasn't linear and I couldn't notate it the way I did it. I wonder if the below notation is valid.

(6r2c6=8r2c2)-r2c3=r9c3-(8=123456)r9c145796=>r1c6<>6

[eleven]

Nice move, Ted.

This one is not so nice but long also
(5=4)r8c8-(4=8)r9c139-(8=1)r7c145-(1=5)r178c7 => r9c7<>5
(either r8c8=5 or r8c8=4->r9c9=2->r9c13=38->r7c1=2->r7c45=19->r178c7=258)

Marty, i only can see, that the 6 has to go to r9c6, when i use the 24 in r23c6 too, which comes from a 6 in r2c3.
In band 3 alone there is no reason, that 6 could not be in r9c5.

[Marty R.]

Marty, i only can see, that the 6 has to go to r9c6, when i use the 24 in r23c6 too, which comes from a 6 in r2c3.
In band 3 alone there is no reason, that 6 could not be in r9c5.

Eleven,

Right, I had the 24 pair in c6 from the 6 in r2c3, then I moved down to establish the 8 in r9c3 so r9c6 would see 248 and thus be 6. So I radiated in two directions from box 1 and couldn't notate it that way, so I tried to invent something that might fit. Looking again at my notation, I can see it's not valid.

[eleven]

"And the hero rode off into all directions"
Quoted in a book, i don't remember.

[Marty R.]

"And the hero rode off into all directions"
Quoted in a book, i don't remember.

Possibly this from "Gertrude the Governess"?

"Lord Ronald said nothing; he flung himself from the room, flung himself upon his horse and rode madly off in all directions."

[Leren]

eleven wrote:

SudoQ, this elimination can also be done with
als xz-wing: (6=8r139c3)-(8=6r239c6)=>r1c6<>6
(either r1c3=6 or r13c3=37->r9c3=8->r289c6=246)

Nice move eleven, as a result, I'm now looking for instances of the als xz rule.

Here's one that makes the same eliminations as my first als xy wing but the logic is simpler

Code: Select all

*--------------------------------------------------------------------------------*
|a34      1       367      | 49-5    3679-5 a346      |a25      8      a24       |
| 9       248     68       |b1245   b156    b246      | 7       4-5     3        |
| 5       24      37       | 8       37     b24       | 9       6       1        |
|--------------------------+--------------------------+--------------------------|
| 48      48      5        | 6       2       9        | 3       1       7        |
| 7       6       9        | 3       8       1        | 4       2       5        |
| 1       3       2        | 7       4       5        | 6       9       8        |
|--------------------------+--------------------------+--------------------------|
| 28      5       4        | 129     19      7        | 128     3       6        |
| 6       7       1        | 245     35      2348     | 258     45      9        |
| 238     9       38       | 1245    156     2468     | 1258    7       24       |
*--------------------------------------------------------------------------------*

als xz rule: (5=6) r1c1679 - (6=5) r2c45, r23c6 => r1c45, r2c8 <> 5; stte

Leren

[DonM]

eleven wrote:

SudoQ, this elimination can also be done with
als xz-wing: (6=8r139c3)-(8=6r239c6)=>r1c6<>6
(either r1c3=6 or r13c3=37->r9c3=8->r289c6=246)

Nice move eleven, as a result, I'm now looking for als xz wings.
Here's one that makes the same eliminations as my first als xy wing but the logic is simpler
als xz wing: (5=6) r1c1679 - (6=5) r2c45, r23c6 => r1c45, r2c8 <> 5; stte

Leren

There seems to be some confusion in naming being introduced here. If one is using the original ALS naming then if there are 2 sets such as in the above, then it is ALS xz-rule (not xz-wing), if 3 sets then ALS xy-wing, if greater than 3 sets, then ALS xy chain.

However, (fwiw), some time ago I promoted the use of the term, ALS Chains to refer to all 3 of these constructs because, really, the only difference among them is the number of sets:

als-chains-a-tutorial-asi-3-t6443.html

advanced-als-chains-a-tutorial-asi-3b-t30098.html

[eleven]

Probably i should have called it simply an als xz.

Leren, i think i can understand now, what you have fun with.

Marty, just great, that you knew a similar verse, which i also like. But i am sure that there was a hero, i now think it was "and the hero jumped on his horse and ..."