The New Sudoku Players' Forum

[danlm]

Code: Select all

from:
+------+------+------+
|. 3 . |. 9 . |5 . 6 |
|. . . |. . . |8 . 3 |
|2 . 8 |. . . |. 9 . |
+------+------+------+
|. . 7 |. . . |3 . . |
|. . 5 |. 1 . |. . 8 |
|. 6 . |7 . . |. 1 9 |
+------+------+------+
|. . . |4 7 . |. . . |
|. . . |. . 3 |2 6 . |
|6 . . |. 2 . |. . 7 |
+------+------+------+
I reach:
+--------------+------------+--------+
|147  3    14  |128 9  1278 |5  24 6 |
|1479 1459 6   |12  45 127  |8  24 3 |
|2    45   8   |36  36 45   |7  9  1 |
+--------------+------------+--------+
|1489 189  7   |689 46 489  |3  5  2 |
|349  249  5   |239 1  249  |6  7  8 |
|38   6    23  |7   35 258  |4  1  9 |
+--------------+------------+--------+
|138  128  1239|4   7  6    |19 38 5 |
|5    7    19  |19  8  3    |2  6  4 |
|6    48   43  |5   2  19   |19 38 7 |
+--------------+------------+--------+

I solve it like this:

1°) r3c6=5 => r3c2=4 => r1c3=1
2°) r3c6=4 => r5c6=29 and r2c5=5 => r6c5=3 => r5c4=29
which give r5c2<>29 => r5c2=4 => r9c3=4 =>r1c3=1

Therefore r1c3=1 !!

Do you have a shorter way?

[Allan Barker]

Do you have a shorter way?

Yes. One way is that your way can be, or is shorter:

1°) r3c6=5 => r3c2=4 => r1c3=1
2°) r3c6=4 => r5c6=29 and r2c5=5 => r6c5=3 => r5c4=29
which give r5c2<>29 => r5c2=4 => r9c3=4 =>r1c3=1

Therefore r29c2<>4 => r9c3=4 => r1c3=1 ... , which just means the destruction starts earlier.

Another way is a short discontinuous nice loop that directly assigns r1c8=2, again leading to the end of the puzzle.

Code: Select all

+------------------+----------------+---------------+
| 147   3     (14) | 128   9   1278 | 5   (+2-4)  6 |
| 1479  1459  6    | (12)  45  127  | 8   (+4-2)  3 |
| 2     45    8    | 36    36  45   | 7   9       1 |
+------------------+----------------+---------------+
| 1489  189   7    | 689   46  489  | 3   5       2 |
| 349   249   5    | 239   1   249  | 6   7       8 |
| 38    6     23   | 7     35  258  | 4   1       9 |
+------------------+----------------+---------------+
| 138   128   1239 | 4     7   6    | 19  38      5 |
| 5     7     9(1) | 9(1)  8   3    | 2   6       4 |
| 6     48    34   | 5     2   19   | 19  38      7 |
+------------------+----------------+---------------+

.

[daj95376]

Allan Barker: What a difficult way to describe an XY-Chain.

Code: Select all

 XY-Chain a-b-c-d-e => [r1c46],[r2c8]<>2
 +--------------------------------------------------------------+
 |  147   3    b14    |  18-2  9     178-2 |  5    a24    6     |
 |  1479  1459  6     | e12    45    127   |  8     4-2   3     |
 |  2     45    8     |  36    36    45    |  7     9     1     |
 |--------------------+--------------------+--------------------|
 |  1489  189   7     |  689   46    489   |  3     5     2     |
 |  349   249   5     |  239   1     249   |  6     7     8     |
 |  38    6     23    |  7     35    258   |  4     1     9     |
 |--------------------+--------------------+--------------------|
 |  138   128   1239  |  4     7     6     |  19    38    5     |
 |  5     7    c19    | d19    8     3     |  2     6     4     |
 |  6     48    34    |  5     2     19    |  19    38    7     |
 +--------------------------------------------------------------+
 # 63 eliminations remain


Leaving [r2c8]=4 and additional Singles to complete the puzzle.

[aran]

Allan Barker: What a difficult way to describe an XY-Chain.

Code: Select all

 XY-Chain a-b-c-d-e => [r1c46],[r2c8]<>2
 +--------------------------------------------------------------+
 |  147   3    b14    |  18-2  9     178-2 |  5    a24    6     |
 |  1479  1459  6     | e12    45    127   |  8     4-2   3     |
 |  2     45    8     |  36    36    45    |  7     9     1     |
 |--------------------+--------------------+--------------------|
 |  1489  189   7     |  689   46    489   |  3     5     2     |
 |  349   249   5     |  239   1     249   |  6     7     8     |
 |  38    6     23    |  7     35    258   |  4     1     9     |
 |--------------------+--------------------+--------------------|
 |  138   128   1239  |  4     7     6     |  19    38    5     |
 |  5     7    c19    | d19    8     3     |  2     6     4     |
 |  6     48    34    |  5     2     19    |  19    38    7     |
 +--------------------------------------------------------------+
 # 63 eliminations remain


Leaving [r2c8]=4 and additional Singles to complete the puzzle.

Allan Barker wasn't describing an XY chain : as he said he had in mind the discontinuous loop which concludes on 2r1c8 : sharper than your XY chain which needs to make eliminations first getting there.

[ronk]

Allan Barker: What a difficult way to describe an XY-Chain.

XY-Chain a-b-c-d-e => [r1c46],[r2c8]<>2
[...]
Leaving [r2c8]=4 and additional Singles to complete the puzzle.

Hmm, using a bilocal does result in Allan's (unwritten) nice loop that is shorter by one strong inference.

r2c8 =4= r1c8 -4- r1c3 -1- r8c3 =1= r8c4 -1- r2c4 -2- r2c8 ==> r2c8<>2

Interestingly, I don't think there are nice loop rules that directly result in assignments r2c8=4 or r1c8=2.

[udosuk]

Allan Barker: What a difficult way to describe an XY-Chain.

Code: Select all

 XY-Chain a-b-c-d-e => [r1c46],[r2c8]<>2
 +--------------------------------------------------------------+
 |  147   3    b14    |  18-2  9     178-2 |  5    a24    6     |
 |  1479  1459  6     | e12    45    127   |  8     4-2   3     |
 |  2     45    8     |  36    36    45    |  7     9     1     |
 |--------------------+--------------------+--------------------|
 |  1489  189   7     |  689   46    489   |  3     5     2     |
 |  349   249   5     |  239   1     249   |  6     7     8     |
 |  38    6     23    |  7     35    258   |  4     1     9     |
 |--------------------+--------------------+--------------------|
 |  138   128   1239  |  4     7     6     |  19    38    5     |
 |  5     7    c19    | d19    8     3     |  2     6     4     |
 |  6     48    34    |  5     2     19    |  19    38    7     |
 +--------------------------------------------------------------+

Of course, your xy-chain only tells half of the story:

Code: Select all

XY-Chain b-c-d-e-f => [r1c8],[r2c12]<>4
+--------------------+--------------------+--------------------+
|  147   3    b14    |  128   9     1278  |  5    -42    6     |
| -4179 -4159  6     | e12    45    127   |  8    f24    3     |
|  2     45    8     |  36    36    45    |  7     9     1     |
+--------------------+--------------------+--------------------+
|  1489  189   7     |  689   46    489   |  3     5     2     |
|  349   249   5     |  239   1     249   |  6     7     8     |
|  38    6     23    |  7     35    258   |  4     1     9     |
+--------------------+--------------------+--------------------+
|  138   128   1239  |  4     7     6     |  19    38    5     |
|  5     7    c19    | d19    8     3     |  2     6     4     |
|  6     48    34    |  5     2     19    |  19    38    7     |
+--------------------+--------------------+--------------------+

But the point is, using all 6 cells like Allan did enables us to present the move really concisely ("elegance" as Luke is pondering recently):

Presentation 1:
r8c34<>[99] => r1c3+r2c4<>[11] => r12c8<>[42] => r12c8=[24]

Presentation 2:
r18c3<>[11] => r1c8+r8c4<>[49] => r2c48<>[12] => r2c8=4

Presentation 3:
r28c4<>[11] => r2c8+r8c3<>[29] => r1c38<>[14] => r1c8=2

[danlm]

Thank you to all for your comments.
All very interresting for me...

The XY-Chain is very new for me... I discover it today...

The Allan's explanations are very helpfull.

DanLM

[Allan Barker]

Interestingly, I don't think there are nice loop rules that directly result in assignments r2c8=4 or r1c8=2.

Ah, I see your point, my reasoning is by analogy. One of the 3 types of discontinuous nice loops (ref: Sudopedia) ends up with two strong links connecting to a target candidate, which is then assigned.

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Sudopedia example of DNL with 2 strong inferences to target candidate:

[r4c2]=8=[r6c2]=6=[r6c8]-6-[r5c8]-2-[r5c5]=2=[r4c5]=8=[r4c2] => r4c2=8

In this Sudopedia example, both terminating strong links are through digit 8 and connect to candidate 8r4c2, which is thus directly assigned. By analogy, my loop (which I should have written out) would be something like this.

(2)r1c8 -4- r1c3 -1- r8c3 =1= r8c4 -1- r2c4 -2- r2c8=2=r1c8 ==> r1c8=2

where one of the two strong links connecting to 2r1c8 is cell r1c8, thus there are two strong links connecting to candidate 2r1c8. A slight variation of this loop assigns the other candidate 4r2c8.
.
.

[daj95376]

By analogy, my loop (which I should have written out) would be something like this.

(2)r1c8 -4- r1c3 -1- r8c3 =1= r8c4 -1- r2c4 -2- r2c8=2=r1c8 ==> r1c8=2

where one of the two strong links connecting to 2r1c8 is cell r1c8, thus there are two strong links connecting to candidate 2r1c8. A slight variation of this loop assigns the other candidate 4r2c8.

Okay, skipping over the 9s in my XY-Chain, there's an MJ AIC that gets the job done by using the green portion of Allan's loop.

Code: Select all

2- r1c8 -4- r1c3 -1- r8c3 =1= r8c4 -1- r2c4 -2   => r2c8<>2

(2=4)r1c8 - (4=1)r1c3 - (1)8rc3=r8c4 - (1=2)r2c4 => r2c8<>2


Soap Box: It seems to me that if everyone wants their AICs to loop, then they really should be called AILs.

[aran]

(2)r1c8 -4- r1c3 -1- r8c3 =1= r8c4 -1- r2c4 -2- r2c8=2=r1c8 ==> r1c8=2

where one of the two strong links connecting to 2r1c8 is cell r1c8, thus there are two strong links connecting to candidate 2r1c8.

Even though it's not my language, I rather think your NL loop should start off 2r1c8=.
On NL : whenever I read of links around the target cell in an NL loop being examined to work out what the verdict is, I am always amazed...the logic in alternating link notation seems so much more straightforward.
Yes I know one is not supposed to comment on NL but...

Presentation 1:
r8c34<>[99] => r1c3+r2c4<>[11] => r12c8<>[42] => r12c8=[24]

Presentation 2:
r18c3<>[11] => r1c8+r8c4<>[49] => r2c48<>[12] => r2c8=4

Presentation 3:
r28c4<>[11] => r2c8+r8c3<>[29] => r1c38<>[14] => r1c8=2

Interesting way of looking at it.
i'm sure you agree that any XY-chain of even length can be presented in that style (ie draw the contradiction from the mid-point nodes then work back).