The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|..8|
 |.7.|.1.|.92|
 |..9|..2|7..|
 |---+---+---|
 |4.7|...|9..|
 |3..|..6|...|
 |...|...|4.6|
 |---+---+---|
 |52.|.43|.1.|
 |.4.|.5.|...|
 |...|.7.|.3.|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 2     35    4     | 357   39    79    | 1     6     8     |
 | 68    7     56    | 58    1     4     | 3     9     2     |
 | 18    138   9     | 38    6     2     | 7     4     5     |
 *-------------------+-------------------+-------------------|
 | 4     6     7     | 1    *28    5     | 9    *28    3     |
 | 3     589   25    | 4    *9-28  6     |*28    7     1     |
 | 189   189   12    | 37    2389  79    | 4     5     6     |
 *-------------------+-------------------+-------------------|
 | 5     2     8     | 9     4     3     | 6     1     7     |
 | 7     4     3     | 6     5     1     |*28   *28    9     |
 | 169   19    16    | 2     7     8     | 5     3     4     |
 *-----------------------------------------------------------*


L-shaped DP, r4c58,r5c57,r8c78 => -28 r5c5 ; stte

[bat999]

Code: Select all

.---------------.----------------.-----------.
| 2    *5-3  4  | 357  *39    79 | 1   6   8 |
| 68    7    56 | 58    1     4  | 3   9   2 |
| 18    138  9  | 38    6     2  | 7   4   5 |
:---------------+----------------+-----------:
| 4     6    7  | 1     28    5  | 9   28  3 |
| 3    *589  25 | 4     289   6  | 28  7   1 |
| 189   189  12 | 37    2389  79 | 4   5   6 |
:---------------+----------------+-----------:
| 5     2    8  | 9     4     3  | 6   1   7 |
| 7     4    3  | 6     5     1  | 28  28  9 |
| 169   19   16 | 2     7     8  | 5   3   4 |
'---------------'----------------'-----------'

There's a contradiction if r1c2 is 3.
r5c2 becomes 5 and r1c5 becomes 9, so there are no 9s left on row 5.
=> -3 r1c2 ; stte

[Marty R.]

Code: Select all

+------------+-------------+---------+
| 2   35  4  | 357 39   79 | 1  6  8 |
| 68  7   56 | 58  1    4  | 3  9  2 |
| 18  138 9  | 38  6    2  | 7  4  5 |
+------------+-------------+---------+
| 4   6   7  | 1   28   5  | 9  28 3 |
| 3   589 25 | 4   289  6  | 28 7  1 |
| 189 189 12 | 37  2389 79 | 4  5  6 |
+------------+-------------+---------+
| 5   2   8  | 9   4    3  | 6  1  7 |
| 7   4   3  | 6   5    1  | 28 28 9 |
| 169 19  16 | 2   7    8  | 5  3  4 |
+------------+-------------+---------+


Play this puzzle online at the Daily Sudoku site

DP (18)r36c12: 3r3c2=9r6c12-(9=7)r6c6,-(7=9)r1c6-(9=3)r1c5=>r1c2,r3c4<>3

[pjb]

Code: Select all

 2      a5-3     4      | 357   d39     79     | 1      6      8     
 68      7       56     | 58     1      4      | 3      9      2     
 18      138     9      | 38     6      2      | 7      4      5     
------------------------+----------------------+---------------------
 4       6       7      | 1      28     5      | 9      28     3     
 3      b589     25     | 4     c289    6      | 28     7      1     
 189     189     12     | 37     2389   79     | 4      5      6     
------------------------+----------------------+---------------------
 5       2       8      | 9      4      3      | 6      1      7     
 7       4       3      | 6      5      1      | 28     28     9     
 169     19      16     | 2      7      8      | 5      3      4     


Chain equivalent of bat999's?
(5)r1c2 = (5-9)r5c2 = r5c5 - (9=3)r1c5 => -3 r1c2; stte
I also first came up with 3r3c2 = 9r6c12 - (9=7)r6c6 - (7=3)r6c = > -3 r3c4; stte; too close to Marty's
Phil

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 2    a35    4      |f37-5 d39   e79     | 1     6     8      |
| 68    7     56     | 58    1     4      | 3     9     2      |
| 18    138   9      | 38    6     2      | 7     4     5      |
|--------------------+--------------------+--------------------|
| 4     6     7      | 1     28    5      | 9     28    3      |
| 3    b589   25     | 4    c289   6      | 28    7     1      |
| 189   189   12     | 37    2389  79     | 4     5     6      |
|--------------------+--------------------+--------------------|
| 5     2     8      | 9     4     3      | 6     1     7      |
| 7     4     3      | 6     5     1      | 28    28    9      |
| 169   19    16     | 2     7     8      | 5     3     4      |
*--------------------------------------------------------------*

(5) r1c2 = (5-9) r5c2 = r5c5 - r1c5 = (9-7) r1c6 = (7) r1c4 => - 5 r1c4; stte

Leren

[Ngisa]

Code: Select all

+------------+-------------+---------+
| 2   d35  4  | 357 a39   79 | 1  6  8 |
| 68  7   56 | 58  1    4  | 3  9  2 |
| 18  e138 9  | f8-3  6    2  | 7  4  5 |
+------------+-------------+---------+
| 4   6   7  | 1   28   5  | 9  28 3 |
| 3   c589 25 | 4   b289  6  | 28 7  1 |
| 189 189 12 | 37  2389 79 | 4  5  6 |
+------------+-------------+---------+
| 5   2   8  | 9   4    3  | 6  1  7 |
| 7   4   3  | 6   5    1  | 28 28 9 |
| 169 19  16 | 2   7    8  | 5  3  4 |
+------------+-------------+---------+


(3=9)r1c5-r5c5=(9-5)r5c2=(5-3)r1c2=r3c2-(3=8)r3c4 => -3r3c4; stte

[bat999]

... Chain equivalent of bat999's?
(5)r1c2 = (5-9)r5c2 = r5c5 - (9=3)r1c5 => -3 r1c2; stte...

Yes, I understand now.
It is an example of the Type 3 Discontinuous Nice Loop described here ---> http://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm

"If the first square has a weak link and a strong link with different candidates, then the weak link's candidate can be eliminated from the square."

In this case...
The weak link of r1c2 is 3 (from r1c5) and the strong link of r1c2 is 5 (to r5c2).

So if r1c2 is not 5 then the 3 can be eliminated from r1c2.
But that would leave no candidates left in r1c2, there's the contradiction.
Must keep that 5 in r1c2.
=> -3 r1c2; stte

[eleven]

Bat,

not that i want to advertise it, but if you look at the AIC you can clearly see, that either (5)r1c2 or (3)r1c5 must be true (or both).
(That's what you found out, too.)
In both cases 3 cannot be in r1c2.

PS: Note, that if you have such a link aX=bY ("a in X or b in Y"), where X and Y see one another, you can both eliminate a from Y and b from X (as in L-wings).

[bat999]

... but if you look at the AIC you can clearly see...

Hi
Your post didn't help me.
Maybe I'll look back at it another time.

[bat999]

...PS: Note, that if you have such a link aX=bY ("a in X or b in Y"), where X and Y see one another, you can both eliminate a from Y and b from X ...

Yes, I can see this now. Another rule to remember.
But the Type 3 Discontinuous Nice Loop does it automatically...
It adds the last link to the chain (from r1c5 to r1c2) and returns to the start square to zap the candidate.

It seems to be a matter of preference...
Some people in this forum are comfortable to express almost anything as an AIC in Eureka notation.
And some people are not.

[daj95376]

...PS: Note, that if you have such a link aX=bY ("a in X or b in Y"), where X and Y see one another, you can both eliminate a from Y and b from X ...

Yes, I can see this now. Another rule to remember.
But the Type 3 Discontinuous Nice Loop does it automatically...
It adds the last link to the chain (from r1c5 to r1c2) and returns to the start square to zap the candidate.

It seems to be a matter of preference...
Some people in this forum are comfortable to express almost anything as an AIC in Eureka notation.
And some people are not.

Not quite.

Although a Type 3 Discontinuous Nice Loop is often effective, there are times when it falls short. Consider the following puzzle.

Code: Select all

 +-----------------------+
 | . 4 . | . . . | . . . |
 | . . . | . . 3 | . . 7 |
 | . . 7 | 8 1 . | . 5 9 |
 |-------+-------+-------|
 | 5 1 . | 7 . . | . . 3 |
 | . 6 9 | . . . | 5 7 . |
 | 4 . . | . . 5 | . 1 2 |
 |-------+-------+-------|
 | 6 5 . | . 9 7 | 3 . . |
 | 8 . . | 5 . . | . . . |
 | . . . | . . . | . 4 . |
 +-----------------------+   # June 25, 2015

 +--------------------------------------------------------------+
 |  19    4     5     | e269   7    f269   |  16    3     8     |
 |  19    8     6     | c49    5     3     |  14    2     7     |
 |  23    23    7     |  8     1     46    |  46    5     9     |
 |--------------------+--------------------+--------------------|
 |  5     1     28    |  7     24   a249   |  89    6     3     |
 |  23    6     9     |  123   238   128   |  5     7     4     |
 |  4     7     38    | b369   36    5     |  89    1     2     |
 |--------------------+--------------------+--------------------|
 |  6     5     24    | d24    9     7     |  3     8     1     |
 |  8     23    1234  |  5     234   124   |  7     9     6     |
 |  7     9     13    |  136   368   168   |  2     4     5     |
 +--------------------------------------------------------------+
 # 47 eliminations remain


Here is a chain in Eureka notation that duplicates a Type 3 Discontinuous Nice Loop for its single elimination -- -2r4c6.

Code: Select all

 (9)r4c6 = (9)r6c4 - (9=4)r2c4 - (4=2)r7c4 - (2)r1c4 = (2)r1c6 - (2)r4c6


This elimination doesn't advance you any further. Now, drop the final weak link, and you have the AIC logic:

Code: Select all

 (9)r4c6 = (9)r6c4 - (9=4)r2c4 - (4=2)r7c4 - (2)r1c4 = (2)r1c6  =>  -2 r4c6 & -9 r1c6


The additional elimination cracks the puzzle and it solves with Singles.


Yes, you could have started a Type 3 Discontinuous Nice Loop at (2)r1c6 and derived -9r1c6, but that's a separate chain that you might have missed. Also, it sometimes takes both eliminations to crack a puzzle. That's one step/chain for AIC, and two steps/chains using Type 3 Discontinuous Loops.

_

[bat999]

...Although a Type 3 Discontinuous Nice Loop is often effective, there are times when it falls short. Consider the following puzzle...

Yes daj, that's a good example.
The AIC from left to right zaps the 9 at r1c4 continues to put the 2 into r1c6 that eliminates the 2 from r4c6.
The AIC from right to left forces 2 into r1c4 and continues to put 9 into r4c6.
Kills two birds with one stone.
Using a Nice Loop would have needed more work to solve the puzzle.

[ronk]

Here is a chain in Eureka notation that duplicates a Type 3 Discontinuous Nice Loop for its single elimination -- -2r4c6.

Code: Select all

 (9)r4c6 = (9)r6c4 - (9=4)r2c4 - (4=2)r7c4 - (2)r1c4 = (2)r1c6 - (2)r4c6


This elimination doesn't advance you any further. Now, drop the final weak link, and you have the AIC logic:

Code: Select all

 (9)r4c6 = (9)r6c4 - (9=4)r2c4 - (4=2)r7c4 - (2)r1c4 = (2)r1c6  =>  -2 r4c6 & -9 r1c6


The additional elimination cracks the puzzle and it solves with Singles.

The AIC from left to right zaps the 9 at r1c4 continues to put the 2 into r1c6 that eliminates the 2 from r4c6.
The AIC from right to left forces 2 into r1c4 and continues to put 9 into r4c6.
Kills two birds with one stone.
Using a Nice Loop would have needed more work to solve the puzzle.

Perhaps not. The following uses "pauses" often seen in AIC notation.

Code: Select all

r1c6 -9- r4c6 =9= r6c4 -9- r2c4 -4- r7c4 -2- r1c4 =2= r1c6 -2- r4c6  ==> r1c6<>9, r4c6<>2

Pause labels could be added, ala David P Bird, but putting the same label on the two appearances of r1c6 seems redundant and pointless. Ditto for r4c6.