The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|5..|...|
 |4..|.6.|..9|
 |76.|.8.|.1.|
 |---+---+---|
 |..8|.1.|4..|
 |.26|.4.|18.|
 |..4|.9.|5..|
 |---+---+---|
 |.1.|.5.|.27|
 |8..|.3.|..1|
 |...|..8|...|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 | 23     9      123    |  5      7-2    1347-2 | 2367   346    8      |
 | 4      8      1235   |ac23     6      137-2  | 237   a35     9      |
 | 7      6      235    | c2349   8     c2349   | 23     1     b45     |
 *----------------------+-----------------------+----------------------|
 | 5      7      8      |  236    1      236    | 4      9      26     |
 | 9      2      6      |  7      4      5      | 1      8      3      |
 | 1      3      4      |  8      9      26     | 5      7      26     |
 *----------------------+-----------------------+----------------------|
 | 36     1      39     |  469    5      469    | 8      2      7      |
 | 8      45     279    |  269    3      2679   | 69     45     1      |
 | 26     45     279    |  1      27     8      | 369    36     45     |
 *---------------------------------------------------------------------*


(2=35)r2c48 - (5=4)r3c9 - (4=392)b2p479 => -2 b2p236 ; stte

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 23    9     123    | 5    c27    12347  | 2367  346   8      |
| 4     8     1235   |d23    6     1237   | 237   5-3   9      |
| 7     6     235    | 2349  8     2349   | 23    1     45     |
|--------------------+--------------------+--------------------|
| 5     7     8      | 236   1     236    | 4     9     26     |
| 9     2     6      | 7     4     5      | 1     8     3      |
| 1     3     4      | 8     9     26     | 5     7     26     |
|--------------------+--------------------+--------------------|
| 36    1     39     | 469   5     469    | 8     2     7      |
| 8     45    279    | 269   3     2679   | 69    45    1      |
|a26    45    279    | 1    b27    8      | 369  a36    45     |
*--------------------------------------------------------------*

(3=2) r9c18 - r9c5 = r1c5 - (2=3) r2c4 => - 3 r2c8; stte

Leren

[Marty R.]

Code: Select all

+------------+---------------+-------------+
| 23 9  123  | 5    27 12347 | 2367 346 8  |
| 4  8  1235 | 23   6  1237  | 237  35  9  |
| 7  6  235  | 2349 8  2349  | 23   1   45 |
+------------+---------------+-------------+
| 5  7  8    | 236  1  236   | 4    9   26 |
| 9  2  6    | 7    4  5     | 1    8   3  |
| 1  3  4    | 8    9  26    | 5    7   26 |
+------------+---------------+-------------+
| 36 1  39   | 469  5  469   | 8    2   7  |
| 8  45 279  | 269  3  2679  | 69   456 1  |
| 26 45 279  | 1    27 8     | 369  36  45 |
+------------+---------------+-------------+


Play this puzzle online at the Daily Sudoku site

DP (49)r37c46: 23r3c46=6r7c46 yields common outcomes.

Pseudo cell (23) in r3c46. (23=5)c4673-(5=4)r3c9-(4=23497)r3c46,r2c4,r1c5

6r7c46-(6=3)r7c1-(3=2)r1c1-(2=7)r1c5-(7=2)r9c5-(2=6)r9c1-(6=3)r9c8-(3=5)r2c8-(5=4)r3c9=>r3c9=4,r1c5=7

[pjb]

Code: Select all

 23      9       123    | 5     d27     12347  | 2367  a36-4   8     
 4       8       1235   |e23     6      1237   | 237   e35     9     
 7       6       235    | 2349   8      2349   | 23     1     f45     
------------------------+----------------------+---------------------
 5       7       8      | 236    1      236    | 4      9      26     
 9       2       6      | 7      4      5      | 1      8      3     
 1       3       4      | 8      9      26     | 5      7      26     
------------------------+----------------------+---------------------
 36      1       39     | 469    5      469    | 8      2      7     
 8       45      279    | 269    3      2679   | 69     45     1     
c26      45      279    | 1     c27     8      | 369   b36     45     


(6)r1c8 = r9c8 - (6=7)r9c15 - (7=2)r1c5 = (2=5)r2c48 - (5=4)r3c9 => -4 r1c8; stte

Phil

PS typo correctd

[bat999]

Code: Select all

 23      9       123    | 5     d27     12347  | 2367  a36-4   8     
 4       8       1235   |e23     6      1237   | 237   e35     9     
 7       6       235    | 2349   8      2349   | 23     1     f45     
------------------------+----------------------+---------------------
 5       7       8      | 236    1      236    | 4      9      26     
 9       2       6      | 7      4      5      | 1      8      3     
 1       3       4      | 8      9      26     | 5      7      26     
------------------------+----------------------+---------------------
 36      1       39     | 469    5      469    | 8      2      7     
 8       45      279    | 269    3      2679   | 69     45     1     
b26      45      279    | 1     c27     8      | 369   b36     45     


(6)r1c8 = r9c8 - (6=7)r9c15 - (7=2)r1c5 = (2=5)r2c48 - (5=4)r3c9 => -4 r1c8; stte

Phil

Aha
Looks like this is the Type 3 Discontinuous Nice Loop expressed in Eureka notation.
"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...
If r1c8 is not 6 then r1c8 is not 4.
=> -4 r1c8; stte

[SteveG48]

Code: Select all

 23      9       123    | 5     d27     12347  | 2367  a36-4   8     
 4       8       1235   |e23     6      1237   | 237   e35     9     
 7       6       235    | 2349   8      2349   | 23     1     f45     
------------------------+----------------------+---------------------
 5       7       8      | 236    1      236    | 4      9      26     
 9       2       6      | 7      4      5      | 1      8      3     
 1       3       4      | 8      9      26     | 5      7      26     
------------------------+----------------------+---------------------
 36      1       39     | 469    5      469    | 8      2      7     
 8       45      279    | 269    3      2679   | 69     45     1     
b26      45      279    | 1     c27     8      | 369   b36     45     


(6)r1c8 - r9c8 - (6=7)r9c15 - (7=2)r1c5 = (2=5)r2c48 - (5=4)r3c9 => -4 r1c8; stte

Phil

Aha
Looks like this is the Type 3 Discontinuous Nice Loop expressed in Eureka notation.
"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...
If r1c8 is not 6 then r1c8 is not 4.
=> -4 r1c8; stte

Bat, I don't understand, and I'd like to. You've quoted this rule about Nice loops a couple of times now, but I don't recognize it. If I try to apply it, I see that the first square actually has strong links with both 6 and 4 to r9c8 and r3c9 respectively. Since a strong link can also be treated as a weak link, your rule would seem to eliminate both 4 and 6 at r1c8, but only one of those is correct. I also don't see this as a discontinuous loop, which is one that's defined as ending in a contradiction. Here we see from Phil's chain that if r1c8 is not a 6 then it's also not a 4. We can't "close the loop", so it's discontinuous in that sense, but there is no contradiction.

We can conclude that r1c8 is not a 4, which is what Phil has done. The rule that applies here is if cell1 and cell2 are in the same house, then (a)[cell1] = (b)[cell2] => -a cell 2 and -b cell1.

[bat999]

Bat, I don't understand, and I'd like to. You've quoted this rule about Nice loops a couple of times now, but I don't recognize it...

Code: Select all

 23      9       123    | 5     d27     12347  | 2367  a36-4   8     
 4       8       1235   |e23     6      1237   | 237   e35     9     
 7       6       235    | 2349   8      2349   | 23     1     f45     
------------------------+----------------------+---------------------
 5       7       8      | 236    1      236    | 4      9      26     
 9       2       6      | 7      4      5      | 1      8      3     
 1       3       4      | 8      9      26     | 5      7      26     
------------------------+----------------------+---------------------
 36      1       39     | 469    5      469    | 8      2      7     
 8       45      279    | 269    3      2679   | 69     45     1     
c26      45      279    | 1     c27     8      | 369   b36     45     


Hi

Information about the Type 3 Discontinuous Nice Loop found here ---> http://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm#types

This is how I figured it...

If r1c8 is not 6 then r9c8 is 6.
That's the strong link from r1c8 to r9c8 (candidate is 6).

So r9c1 is 2
and r9c5 is 7
and r1c5 is 2
and r3c4 is 3
and r3c8 is 5
and r3c9 is 4

If r3c9 is 4 then r1c8 is not 4.
That's the weak link to r1c8 from r3c9 (candidate is 4).

"...the weak link's candidate can be eliminated from the square."

=> -4 r1c8; stte

Maybe you would eliminate the 4 because we can't have two 4s in box 3, without even thinking about Discontinuous Loops.
No explanation was given in Phil's answer, unless it's implied somewhere in that notation.

[daj95376]

[Withdrawn: I don't really want to be in the middle of this.]

_

[SteveG48]

Maybe you would eliminate the 4 because we can't have two 4s in box 3, without even thinking about Discontinuous Loops.
No explanation was given in Phil's answer, unless it's implied somewhere in that notation.

Thanks, Bat. I understand the tutorial (though I don't care for that notation). You can't eliminate the 6 in r1c8 because Phil's loop doesn't run backwards starting with a strong link from 4 in r1c8.

As for the explanation of Phil's answer, he's using the form that I quoted before: (a)[cell1] = (b)[cell2] => -a cell 2 and -b cell1 . His chain establishes the (6)r1c8 = (4)r3c9, eliminating 4 in r1c8 and 6 in r3c9 (if there was one). Think of it this way. If r1c8 is not a 6, then the chain shows that r3c9 is a 4, but that means that r1c8 couldn't be a 4. On the other hand, if r1c8 is a 6, then it can't be a 4. Either way, r1c8 is not a 4. Then, since strong links work both ways, it follows by the same logic that r3c9 can't be a 6- but we already knew that.

[daj95376]

[Withdrawn: I don't really want to be in the middle of this.]

_

[pjb]

Getting back to my chain, the logic is quite straightforward:
if 6 at r1c8 is true , then 4 at r1c8 if false
if 6 at r1c8 is false, then via the chain 4 at r3c9 is true,and therefore 4 at r1c8 is false
either way 4 at r1c8 is false

Phil

[Sudtyro2]

Code: Select all

*--------------------------------------------------------------*
| 2-3   9     123    | 5    b27    12347  | 2367  346   8      |
| 4     8     1235   |b23    6     1237   | 237   35    9      |
| 7     6     235    |a2349  8    a2349   | 23    1     45     |
|--------------------+--------------------+--------------------|
| 5     7     8      | 236   1     236    | 4     9     26     |
| 9     2     6      | 7     4     5      | 1     8     3      |
| 1     3     4      | 8     9     26     | 5     7     26     |
|--------------------+--------------------+--------------------|
|d36B   1     39A    | 469   5     469    | 8     2     7      |
| 8     45    279    | 269   3     2679   | 69    45    1      |
|d26    45    279    | 1    c27    8      | 369   36    45     |
*--------------------------------------------------------------*

An alternate common conclusion for Marty's AUR(49)r37c46.
Use internals for r3c46 and externals for r7c46.

Code: Select all

(2|3)r3c46 – (23=7)b2p24 – (7=2)r9c5 – (2=63)r79c1 – 3r1c1; stte
     ||                                            /
(9-3)r7c3 = 3r7c1 --------------------------------

SteveC