The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|..5|2.9|
 |...|..7|.53|
 |..8|.9.|...|
 |---+---+---|
 |...|..3|..4|
 |.5.|.7.|.8.|
 |9..|6..|...|
 |---+---+---|
 |...|.1.|6..|
 |17.|9..|...|
 |2.3|4..|...|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 3467    1346    1467   | 8      46     5      | 2      14     9     
 46      1469    1469   | 12     246    7      | 8      5      3     
 5       2       8      | 3      9      14     | 147    1467   167   
------------------------+----------------------+---------------------
 678     168     1267   | 5      28     3      | 179    12679  4     
 346     5       1246   | 12     7      9      | 13     8      126   
 9       138     127    | 6      248    14     | 1357   127    1257   
------------------------+----------------------+---------------------
 48      489     459    | 7      1     *28     | 6      3     *58-2   
 1       7       56     | 9      3     *68-2   | 45     24    *58-2   
 2       68      3      | 4      5      68     | 179    179    17     


DP (28) at r78c69 => -2 r78c9, r8c6; stte

Phil

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 3467  1346  1467   | 8     46    5      | 2     14    9      |
| 46    1469  1469   | 12    246   7      | 8     5     3      |
| 5     2     8      | 3     9     1-4    |a147   1467  167    |
|--------------------+--------------------+--------------------|
| 678   168   1267   | 5     28    3      | 179   12679 4      |
| 346   5     1246   | 12    7     9      | 13    8     126    |
| 9    d138   127    | 6     e48  f14     |c1357  127   1257   |
|--------------------+--------------------+--------------------|
| 48    489   459    | 7     1     28     | 6     3     258    |
| 1     7     56     | 9     3     268    |b45    24    258    |
| 2     68    3      | 4     5     68     | 179   179   17     |
*--------------------------------------------------------------*

(4) r3c7 = (4-5) r8c7 = (5-3) r6c7 = (3-8) r6c2 = (8-4) r6c5 = (4) r6c6 => - 4 r3c6; stte

Leren

[Marty R.]

Code: Select all

+----------------+------------+-----------------+
| 3467 1346 1467 | 8  46  5   | 2    14    9    |
| 46   1469 1469 | 12 246 7   | 8    5     3    |
| 5    2    8    | 3  9   14  | 147  1467  167  |
+----------------+------------+-----------------+
| 678  168  1267 | 5  28  3   | 179  12679 4    |
| 346  5    1246 | 12 7   9   | 13   8     126  |
| 9    138  127  | 6  248 14  | 1357 127   1257 |
+----------------+------------+-----------------+
| 48   489  459  | 7  1   28  | 6    3     258  |
| 1    7    56   | 9  3   268 | 45   24    258  |
| 2    68   3    | 4  5   68  | 179  179   17   |
+----------------+------------+-----------------+


Play this puzzle online at the Daily Sudoku site

DP (28)r78c69

6r8c6=5r78c9-(5=4)r8c7-(4=1793)r3495c7-(3=468)r257c1-(8=6)r9c2=> -6r8c3,r9c6

[Marty R.]

Phil,

You handled that DP a little more efficiently than I did.

[pjb]

Marty

I spent ages looking for an external solution likes yours without luck before I looked at the internals.

Phil

[bat999]

Code: Select all

.-------------------.----------------.--------------------.
|  3467  1346  1467 |  8    46   5   |  2     14     9    |
| c46    1469  1469 |  12   246  7   |  8     5      3    |
|  5     2     8    |  3    9    14  |  147   1467   167  |
:-------------------+----------------+--------------------:
|  67-8  168   1267 |  5   a28   3   |  179   12679  4    |
| c346   5     1246 | a12   7    9   | b13    8      126  |
|  9     138   127  |  6    248  14  |  1357  127    1257 |
:-------------------+----------------+--------------------:
| d48    489   459  |  7    1    28  |  6     3      258  |
|  1     7     56   |  9    3    268 |  45    24     258  |
|  2     68    3    |  4    5    68  |  179   179    17   |
'-------------------'----------------'--------------------'

(8=1)r4c5,r5c4 - (1=3)r5c7 - (3=64)r25c1 - (4=8)r7c1 => -8 r4c1; stte

[eleven]

DP (28)r78c69

6r8c6=5r78c9-(5=4)r8c7-(4=1793)r3495c7-(3=468)r257c1-(8=6)r9c2=> -6r8c3,r9c6

Alternatively: DP 28r78c69: 6r8c6=2r8c8 (internal b8, external b9)
2r8c8=6r8c6-(6=542)r8c378 => r8c8=2

[Sudtyro2]

Phil, sorry to be so slow (twice) on a Monday morning...

Relative to your comment to Marty, I think his solution used internals (6r8c6 and 5r78c9), so I assume your solution used externals. But, I can't pick out what externals you used since no chain was given. Help?

SteveC

[Marty R.]

Phil, sorry to be so slow (twice) on a Monday morning...

Relative to your comment to Marty, I think his solution used internals (6r8c6 and 5r78c9), so I assume your solution used externals. But, I can't pick out what externals you used since no chain was given. Help?

SteveC

I think Phil's solution leaves too much to the reader's imagination. I think he treated col. 9 as if the UR was a Type 4. Since 8 is a strong link, the 2's are removed to kill the DP, but I don't think that move is actually played without further analysis unless the other two cells are both bivalues. I wish I had thought of the Type 4 angle, but I didn't . If I did, I think my solution would've been either the 2s are removed from r78rc9 or r8c6=6 (sticking with internals).

-2r78c9=6r8c8 -(6=542)r8c378=> -2r78c9.

The removal of 2 from r8c6 is a natural result of the removal of 2 from r78c9, but is not a DIRECT conclusion from the logic.

[eleven]

It is also called "hidden unique rectangle".
There are strong links for 2 in c6 and r7, and for 8 in r8 and c9, and 28 in r7c6.
This allows you to "directly" eliminate the three 2's, because they lead to a deadly pattern 2-8-2-8 .
2r8c6->8r8c9 and 8r7c6->2r7c9 => r8c6<>2
2r7c9->8r8c9 and 8r7c6->2r8c6 => r7c9<>2
2r8c9->8r8c6 and 8r7c9->2r7c6 => r8c9<>2
Also
8r7c6->2r7c9 and 2r8c6->8r8c9 => r7c6<>8

[blue]

Another way to look at it, is that 2r8c8 is the only "external" that is required. If it was false, there would be hidden pairs for <28> in b9 (in r78c9) and in r8 (in r8c69), and making the corresponding eliminations would produce the (deadly) UR pattern.
Since no other externals are required, it follows that 2r8c8 must be true (and 2r8c6,2r78c9 false).

Edit: typos fixed

[Sudtyro2]

Code: Select all

 3467    1346    1467   | 8      46     5      | 2      14     9     
 46      1469    1469   | 12     246    7      | 8      5      3     
 5       2       8      | 3      9      14     | 147    1467   167   
------------------------+----------------------+---------------------
 678     168     1267   | 5      28     3      | 179    12679  4     
 346     5       1246   | 12     7      9      | 13     8      126   
 9       138     127    | 6      248    14     | 1357   127    1257   
------------------------+----------------------+---------------------
 48      489     459    | 7      1     *28     | 6      3     *58-2   
 1       7       56     | 9      3     *68-2   | 45     24    *58-2   
 2       68      3      | 4      5      68     | 179    179    17

     
Adding one more to the fray...

Keeping with the externals approach, one can look first at the bilocals among the eight UR digits and note that all remain “covered” except for 2r8c9 and 8r7c6. So, borrowing from eleven's b9 external, 2r8c8, we have cover for 2r8c9 and can immediately write

Code: Select all

2r8c8 – 2r78c9,r8c6

B8 gives us cover for 8r7c6 from 8r9c6, and we can get a common outcome from

Code: Select all

8r9c6 – (8=6)r9c2 – (6=452)r8c378 – 2r78c9,r8c6

Note the reuse of eleven's ALS, where his mixed internal/external approach reduces the chains to one short discontinuous loop.
[Edit: reference is being made to eleven's first post]

[Marty R.]

It is also called "hidden unique rectangle".
There are strong links for 2 in c6 and r7, and for 8 in r8 and c9, and 28 in r7c6.
This allows you to "directly" eliminate the three 2's, because they lead to a deadly pattern 2-8-2-8 .
2r8c6->8r8c9 and 8r7c6->2r7c9 => r8c6<>2
2r7c9->8r8c9 and 8r7c6->2r8c6 => r7c9<>2
2r8c9->8r8c6 and 8r7c9->2r7c6 => r8c9<>2
Also
8r7c6->2r7c9 and 2r8c6->8r8c9 => r7c6<>8

Sorry, I can't follow the notation.

From what I can see from the Type 4 and Hiddens, the SL8 in c9 => -2, r78c9, r8c6, which are all three of Phil's eliminations, although I don't know exactly what his line of thinking was

The SL8 in r8 duplicates the -2 r7c9
The sL2 in r7=> -8r8c9
The SL2 in c6 duplicates the -8r8c9
You also show a -8r7c6 which I don't follow

Code: Select all

.-------------------.----------------.--------------------.
|  3467  1346  1467 |  8    46   5   |  2     14     9    |
| c46    1469  1469 |  12   246  7   |  8     5      3    |
|  5     2     8    |  3    9    14  |  147   1467   167  |
:-------------------+----------------+--------------------:
|  67-8  168   1267 |  5   a28   3   |  179   12679  4    |
| c346   5     1246 | a12   7    9   | b13    8      126  |
|  9     138   127  |  6    248  14  |  1357  127    1257 |
:-------------------+----------------+--------------------:
| d48    489   459  |  7    1    28  |  6     3      258  |
|  1     7     56   |  9    3    268 |  45    24     258  |
|  2     68    3    |  4    5    68  |  179   179    17   |
'-------------------'----------------'--------------------'

[ArkieTech]

A good study in Notation.

Code: Select all

 *--------------------------------------------------------------------*
 | 3467   1346   1467   | 8      46     5      | 2      14     9      |
 | 46     1469   1469   | 12     246    7      | 8      5      3      |
 | 5      2      8      | 3      9      14     | 147    1467   167    |
 |----------------------+----------------------+----------------------|
 | 678    168    1267   | 5      28     3      | 179    12679  4      |
 | 346    5      1246   | 12     7      9      | 13     8      126    |
 | 9      138    127    | 6      248    14     | 1357   127    1257   |
 |----------------------+----------------------+----------------------|
 | 48     489    459    | 7      1     *28     | 6      3     *258    |
 | 1      7      56     | 9      3     *268    | 45     24    *258    |
 | 2      68     3      | 4      5      68     | 179    179    17     |
 *--------------------------------------------------------------------*
[(2=5)r8c78-5r78c9
           -(5=28)r8c36]->[dp:28r78c69]->2r8c8; ste