The New Sudoku Players' Forum

[DonM]

it produces an elimination that opens the door to an AUR move that places a digit:

AUR(56)r46c25
||
(12-6)r4c2=r4c5-(6=5)r6c5
||
(2-5)r4c5=(5)r6c5
||
(289)r6c2

=> r6c2<>5->r6c5=5

Looks like something's missing in the (289)r6c2 line.

Silly me, I'm just not seeing what's missing.

Sorry, I never even noticed your intermediate r6c2<>5. I took your "move that places a digit" statement literally ... and expected the last line to read ...

(289-5)r6c2 = (5)r6c5.

Thanks for the clarification. I've made careless mistakes before so I really was concerned that I was missing something.

[Luke]

I read Strm's move as an examination of what happens under all three possibilities for r6c8.

Thanks for that, now I get it. I’m slow but sure. Mainly sure slow.

The chain which you have in mind - in effect the same move seen differently-isn't "complicated" at all to write.

Well, maybe for you, you’re aran! I’m just………..trying. Now, ronk has already expressed this in the notation right proper for SPF (saved and duly noted.) However, considering the loop I see goes in the other direction, and you have thrown down the gauntlet, and it’s St. Paddy’s Day, I offer the following stab:

Code: Select all

 
 *-----------------------------------------------------------------------------*
 | 89      3       5       | 2       7       1       | 4       89      6       |
 | 12489   12489   1289    | 6       89      5       | 7       1289    3       |
 | 1289    7       6       | 4       89      3       | 289     5       128     |
 |-------------------------+-------------------------+-------------------------|
 | 3       1256    12      | 8       256     4       | 25      7       9       |
 | 12458   124568  128     | 9       3       7       | 258     1268    1258    |
 | 7       25689   289     | 1       256     26      | 3       268     4       |
 |-------------------------+-------------------------+-------------------------|
 | 12589   12589   3       | 7       126     26      | 2589    4       258     |
 | 1259    1259    4       | 3       12      8       | 6       29      7       |
 | 6       28      7       | 5       4       9       | 1       3       28      |
 *-----------------------------------------------------------------------------*

Code: Select all

(26)r6c68=(8)r6c8-(8=9)r1c8-(9=2)r8c8-(2=1)r8c5-(1)r7c5=(26)r7c56-(2+6)r6c56=(5)r6c5 =>r6c5<>26.

Don, thanks for the info on the notation. I will study it after corned beef and cabbage at the pub (first things first.) As for this particular UR, I think of these as a pattern with an instant placement. There’s a “strong elbow” as well as a strong link on the non-“elbow” component. The non-“elbow” digit is out, don’t think twice, it’s alright.

Thumb:

[DonM]

Code: Select all

 *--------------------------------------------------------------------*
 |*89     3      5      | 2      7      1      | 4     *89     6      |
 | 12489  12489  1289   | 6     *89     5      | 7     *89+12  3      |
 |*89+12  7      6      | 4     *89     3      |-289    5     #12     |
 |----------------------+----------------------+----------------------|
 | 3      1256   12     | 8      256    4      | 25     7      9      |
 | 2458   24568  28     | 9      3      7      | 258    1268   1258   |
 | 7      25689  289    | 1      256    26     | 3      268    4      |
 |----------------------+----------------------+----------------------|
 | 128    1289   3      | 7      126    26     | 2589   4      258    |
 | 1259   1259   4      | 3      12     8      | 6      29     7      |
 | 6      28     7      | 5      4      9      | 1      3      28     |
 *--------------------------------------------------------------------*

A slightly more elaborate BUG-Lite+2 deduction

BUG-Lite:(89#6)r1c18|r2c58|r3c15
||
(1&2)r3c19
||
(1&2)r2c8|r3c9 => r3c7 <> 2

I love these things. Just wish I was 'seeing' more of them. Am reviewing your 'Between Uniqueness & Bug: Bug-lite' as we speak.

[aran]

I read Strm's move as an examination of what happens under all three possibilities for r6c8.

Thanks for that, now I get it. I’m slow but sure. Mainly sure slow.

The chain which you have in mind - in effect the same move seen differently-isn't "complicated" at all to write.

Well, maybe for you, you’re aran! I’m just………..trying. Now, ronk has already expressed this in the notation right proper for SPF (saved and duly noted.) However, considering the loop I see goes in the other direction, and you have thrown down the gauntlet, and it’s St. Paddy’s Day, I offer the following stab:

Code: Select all

 
 *-----------------------------------------------------------------------------*
 | 89      3       5       | 2       7       1       | 4       89      6       |
 | 12489   12489   1289    | 6       89      5       | 7       1289    3       |
 | 1289    7       6       | 4       89      3       | 289     5       128     |
 |-------------------------+-------------------------+-------------------------|
 | 3       1256    12      | 8       256     4       | 25      7       9       |
 | 12458   124568  128     | 9       3       7       | 258     1268    1258    |
 | 7       25689   289     | 1       256     26      | 3       268     4       |
 |-------------------------+-------------------------+-------------------------|
 | 12589   12589   3       | 7       126     26      | 2589    4       258     |
 | 1259    1259    4       | 3       12      8       | 6       29      7       |
 | 6       28      7       | 5       4       9       | 1       3       28      |
 *-----------------------------------------------------------------------------*

Code: Select all

(26)r6c68=(8)r6c8-(8=9)r1c8-(9=2)r8c8-(2=1)r8c5-(1)r7c5=(26)r7c56-(2+6)r6c56=(5)r6c5 =>r6c5<>26.

Luke
Exactly right. I award you a shamrock

[StrmCkr]

noting fancy here just pointing out some options moves avalilable.

XYZ-Wing: 8/5/2 in r45c7,r5c3 => r5c89<>2
Empty Rectangle: 2 in b6 (r67c6) => r7c7<>2
sashimi x-wing: (8)in R1C18,R6C8,R6C23 => R5C1 <>8

and now more fancy useless stuff.

(8=2)R9C29-(2=1)R3C9-(1=258)r5C379{aALS} => R5C2 <>2

[DonM]

noting fancy here just pointing out some options moves avalilable.

XYZ-Wing: 8/5/2 in r45c7,r5c3 => r5c89<>2
Empty Rectangle: 2 in b6 (r67c6) => r7c7<>2
sashimi x-wing: (8)in R1C18,R6C8,R6C23 => R5C1 <>8

and now more fancy useless stuff.

(8=2)R9C29-(2=1)R3C9-(1=258)r5C379{aALS} => R5C2 <>2

Nice pickup on the Sashimi!. Also, the r7c7<>2 is a clever elimination, but I'm not sure it's what I think of as a classic ER whereby one of the conjugates being true would result in an empty rectangle if the digit for elimination was true. I could be missing it though or maybe the prevailing definition has changed.

[DonM]

(2=8)r5c3-grp(8)r6c23=r6c8-als(8=25)r45c7 (edit: or, better, using strom_norm's xyz-wing) => r5c89<>2

AUR(58)r57c79
||
(2)r5c7-(2=5)r4c7-r5c9=(5)r7c9
||
(29-5)r7c7=(5)r7c9
||
(1)r5c9-(1=2)r3c9-(2=8)r9c9
||
(2)r7c9

=> r7c9<>8

[StrmCkr]

the Empty rectangle is after the xyz wing... only..

ps.

don't forget the xyz-wing in box 6 that removes the 2's in r5c89

storm norm said it first.

i mearly listed where it was.

[ronk]

(2=8)r5c3-grp(8)r6c23=r6c8-als(8=25)r45c7 (edit: or, better, using strom_norm's xyz-wing) => r5c89<>2

AUR(58)r57c79
||
(2)r5c7-(2=5)r4c7-r5c9=(5)r7c9
||
(29-5)r7c7=(5)r7c9
||
(1)r5c9-(1=2)r3c9-(2=8)r9c9
||
(2)r7c9

=> r7c9<>8

Nice. It can be improved with the <5> strong inference in c9. As a bonus, the r5c9<>2 elimination is then not required.

AUR(58)r57c79
||
(2)r5c7 - (2=5)r4c7 - (5)r7c7 = (5)r7c9
||
(29-5)r7c7 = (5)r7c9
||
(12-5)r5c9 = (5)r7c9
||
(2)r7c9

==> r7c9=25

[edit: included DonM's r5c89<>2 intro line into quote]

[DonM]

AUR(58)r57c79
||
(2)r5c7-(2=5)r4c7-r5c9=(5)r7c9
||
(29-5)r7c7=(5)r7c9
||
(1)r5c9-(1=2)r3c9-(2=8)r9c9
||
(2)r7c9

=> r7c9<>8

Nice. It can be improved with the <5> strong inference in c9. As a bonus, the r5c9<>2 elimination is then not required.

AUR(58)r57c79
||
(2)r5c7 - (2=5)r4c7 - (5)r7c7 = (5)r7c9
||
(29-5)r7c7 = (5)r7c9
||
(12-5)r5c9 = (5)r7c9
||
(2)r7c9

==> r7c9=25

Interesting. Never would have occurred to me since the r5c9 was long gone by the time I got to this AUR. Also, the r5c9<>2 is necessary for another chain (unless I can get around it somehow- haven't checked) that ultimately solves the puzzle so I would still need it. But still, it just shows how many alternate possibilites might be lurking.

[Luke]

I see a lot of posts from folks confused about ALS-xz, and I'd like to mention something that helped me out with them: start simple!

The most basic ALS is a single bivalue cell, so the most basic ALS-xz will have a bivalue as one set. If the other set is also small (N+1 where N is 2 or 3) then it gets much easier to spot the pattern:

Code: Select all

 *--------------------------------------------------------------------*
 | 89     3      5      | 2      7      1      | 4      89     6      |
 | 12489  12489  1289   | 6      89     5      | 7      1289   3      |
 | 1289   7      6      | 4      89     3      | 289    5      12     |
 |----------------------+----------------------+----------------------|
 | 3      1256   12     | 8      256    4      | 25     7      9      |
 | 2458   24568  28     | 9      3      7      | 258    1268   1258   |
 | 7      25689  289    | 1      256    26     | 3      268    4      |
 |----------------------+----------------------+----------------------|
 |B128    1-289  3      | 7     B126   B26     | 2589   4      258    |
 | 1259   1259   4      | 3      12     8      | 6      29     7      |
 | 6     A28     7      | 5      4      9      | 1      3      28     |
 *--------------------------------------------------------------------*

The xyz wing could be looked as a bare-bones ALS-xz, and either bivalue cell could serve as set A:

Code: Select all

*--------------------------------------------------------------------*
 | 89     3      5      | 2      7      1      | 4      89     6      |
 | 12489  12489  1289   | 6      89     5      | 7      1289   3      |
 | 1289   7      6      | 4      89     3      | 289    5      12     |
 |----------------------+----------------------+----------------------|
 | 3      1256   12     | 8      256    4      |*25     7      9      |
 | 2458   24568 *28     | 9      3      7      |*258   1-268  1-258   |
 | 7      25689  289    | 1      256    26     | 3      268    4      |
 |----------------------+----------------------+----------------------|
 | 128    1289   3      | 7      126    26     | 2589   4      258    |
 | 1259   1259   4      | 3      12     8      | 6      29     7      |
 | 6      28     7      | 5      4      9      | 1      3      28     |
 *--------------------------------------------------------------------*

I tried to figure a way to wing these two together to impress DonM, but couldn't do it.

After the xyz wing there's another:

Code: Select all

 *--------------------------------------------------------------------*
 | 89     3      5      | 2      7      1      | 4      89     6      |
 | 12489  12489  1289   | 6      89     5      | 7      1289   3      |
 | 1289   7      6      | 4      89     3      |-289    5     A12     |
 |----------------------+----------------------+----------------------|
 | 3      1256   12     | 8      256    4      |B25     7      9      |
 | 2458   24568  28     | 9      3      7      |B258    168  B158     |
 | 7      25689  289    | 1      256    26     | 3      268    4      |
 |----------------------+----------------------+----------------------|
 | 128    1289   3      | 7      126    26     | 2589   4      258    |
 | 1259   1259   4      | 3      12     8      | 6      29     7      |
 | 6      28     7      | 5      4      9      | 1      3      28     |
 *--------------------------------------------------------------------*

Of course, both Myth and aran covered that elim in much cooler ways already, but my point is these basic ones are everywhere. Once one starts seeing the little ones, the bigger ones start coming more easily.

[ronk]

Here are two eliminations in the post-SSTS pencilmarks that I don't think have been posted.

Code: Select all

 89     3      5      | 2      7      1      | 4      89     6
 12489 *2489-1 1289   | 6      89     5      | 7      1289   3
*1289   7      6      | 4      89     3      | 289    5     *12
----------------------+----------------------+--------------------
 3      1256   12     | 8      256    4      | 25     7      9
*2458  *24568  28     | 9      3      7      | 258   *1268  *1258
 7      25689  289    | 1      256    26     | 3      268    4
----------------------+----------------------+--------------------
 128    1289   3      | 7      126    26     | 2589   4      258
*259-1  1259   4      | 3      12     8      | 6      29     7
 6      28     7      | 5      4      9      | 1      3      28

r2c2 =4= r5c2 =6= r5c8 =1= r5c9 -1- r3c9 =1= r3c1 -1- r2c2 ==> r2c2<>1

The chain segment in blue is reused in the following:

r8c1 =5= r5c1 =4= r5c2 =6= r5c8 =1= r5c9 -1- r3c9 =1= r3c1 -1- r8c1 ==> r8c1<>1

Unfortunately, with lots of candidates in r2c2 and r8c1 and lots of digit <1> candidates around, the likelihood of this being useful is slim.

[DonM]

This puzzle is now up for a complete solution if anyone would like to.

[StrmCkr]

meths
BUG-Lite:(89#6)r1c18|r2c58|r3c15
||
(1&2)r3c19
||
(1&2)r2c8|r3c9 => r3c7 <> 2

Naked Pair: 8,9 in r1c8,r3c7 => r2c8<>8, r2c8<>9
Naked Pair: 8,9 in r3c57 => r3c1<>8, r3c1<>9

Skyscraper: 2 in r3c1,r9c2 (connected by r39c9) => r2c2,r78c1<>2

XY-Chain: r1c1 -8- r7c1 -1- r3c1 -2- r3c9 -1- r2c8 -2- r8c8 -9- r1c8 -8- r1c1 => r1c1<>8, r1c1=9 {edited same move but a shorter chain thats to ronk}

singles to the end.