The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|71.|
 |.8.|79.|...|
 |..4|.13|..6|
 |---+---+---|
 |.2.|4..|6.3|
 |.46|.2.|...|
 |..1|..9|...|
 |---+---+---|
 |2..|9..|.6.|
 |7..|...|2..|
 |..9|6..|..1|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 6     9     3      |c258   458   458    | 7     1    d2-8    |
| 1     8     2      | 7     9     6      | 35    34    45     |
| 5     7     4      | 28    1     3      | 9     28    6      |
|--------------------+--------------------+--------------------|
| 89    2     7      | 4     58    1      | 6     589   3      |
| 389   4     6      |b358   2     7      | 1     589  a58     |
| 38    5     1      | 38    6     9      | 4     27    27     |
|--------------------+--------------------+--------------------|
| 2     1     58     | 9     34578 458    | 358   6     457    |
| 7     6     58     | 1     3458  458    | 2     34    9      |
| 4     3     9      | 6     578   2      | 58    57    1      |
*--------------------------------------------------------------*

H2 Wing: (8=5) r5c9 - r5c4 = (5-2) r1c4 = (2) r1c9 => - 8 r1c9; stte

Leren

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 6      9      3      | 258    458    458    | 7      1     a28     |
 | 1      8      2      | 7      9      6      | 35     34     45     |
 | 5      7      4      |d28     1      3      | 9      8-2    6      |
 *----------------------+----------------------+----------------------|
 | 89     2      7      | 4      58     1      | 6      589    3      |
 | 389    4      6      |c358    2      7      | 1      589   b58     |
 | 38     5      1      |c38     6      9      | 4      27     27     |
 *----------------------+----------------------+----------------------|
 | 2      1      58     | 9      34578  458    | 358    6      457    |
 | 7      6      58     | 1      3458   458    | 2      34     9      |
 | 4      3      9      | 6      578    2      | 58     57     1      |
 *--------------------------------------------------------------------*


(2=8)r1c9 - (8=5)r5c9 - (5=38)r56c4 - (8=2)r3c4 => -2 r3c8 ; stte

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 6      9      3      | 258    458    458    | 7      1      28     |
 | 1      8      2      | 7      9      6      | 35     34     45     |
 | 5      7      4      |a28     1      3      | 9     b28     6      |
 *----------------------+----------------------+----------------------|
 | 89     2      7      | 4      58     1      | 6     b589    3      |
 | 389    4      6      |a358    2      7      | 1     b589    8-5    |
 | 38     5      1      |a38     6      9      | 4      27     27     |
 *----------------------+----------------------+----------------------|
 | 2      1      58     | 9      34578  458    | 358    6      457    |
 | 7      6      58     | 1      3458   458    | 2      34     9      |
 | 4      3      9      | 6      578    2      | 58     57     1      |
 *--------------------------------------------------------------------*


(5=238)r356c4 - (2=589)r345c8 => -5 r5c9 ; stte

[pjb]

Code: Select all

6      9      3      |b258    458    458    | 7      1     c28     
1      8      2      | 7      9      6      | 35     34     45     
5      7      4      | 28     1      3      | 9      28     6     
---------------------+----------------------+---------------------
89     2      7      | 4      58     1      | 6      598   3     
389    4      6      |a358    2      7      | 1     e589   d8-5     
38     5      1      | 38     6      9      | 4      27     27     
---------------------+----------------------+---------------------
2      1      58     | 9      34578  458    | 358    6      457   
7      6      58     | 1      3458   458    | 2      34     9     
4      3      9      | 6      578    2      | 58     57     1     


(5)r5c4 = (5-2)r1c4 = (2-8)r1c9 = (8-5)r5c9 = r5c8 => -5 r5c9; stte

Phil

[Marty R.]

Code: Select all

+----------+---------------+-------------+
| 6   9 3  | 258 458   458 | 7   1   28  |
| 1   8 2  | 7   9     6   | 35  34  45  |
| 5   7 4  | 28  1     3   | 9   28  6   |
+----------+---------------+-------------+
| 89  2 7  | 4   58    1   | 6   589 3   |
| 389 4 6  | 358 2     7   | 1   589 58  |
| 38  5 1  | 38  6     9   | 4   27  27  |
+----------+---------------+-------------+
| 2   1 58 | 9   34578 458 | 358 6   457 |
| 7   6 58 | 1   3458  458 | 2   34  9   |
| 4   3 9  | 6   578   2   | 58  57  1   |
+----------+---------------+-------------+


Play this puzzle online at the Daily Sudoku site

Same elimination as Leren, but I played it as a UR (58), r78c36, using externals in c6.

(8=5)r1c6-r1c4=r5c4-(5=8)r5c9=>r1c9<>8

[Ngisa]

Code: Select all

+----------+---------------+---------------+
| 6   9 3  | d258 458   458 | 7   1    e28   |
| 1   8 2  | 7   9     6   | 35  345  45   |
| 5   7 4  | 28  1     3   | 9   28   6    |
+----------+---------------+---------------+
| 89  2 7  | 4   b58    1   | 6   a589  3    |
| 389 4 6  | c358 2     7   | 1   589  589  |
| 38  5 1  | 38  6     9   | 4   27   f27   |
+----------+---------------+---------------+
| 2   1 58 | 9   34578 458 | 358 6    g4578 |
| 7   6 58 | 1   3458  458 | 2   3459 459  |
| 4   3 9  | 6   578   2   | 58  h7-5   1    |
+----------+---------------+---------------+


(5)r4c8=r4c5-r5c4=(5-2)r1c4=(2)r1c9-(2=7)r6c9-r7c9=(7)r9c8 => -5r9c8, stte.

[pjb]

Marty

The type 2 UR (58), r78c36 leads to -4 r1c6 and r78c5. Is this not a separate step prior to executing your nice little chain? Or perhaps I need to learn more about externals?

Phil

[daj95376]

Marty

The type 2 UR (58), r78c36 leads to -4 r1c6 and r78c5. Is this not a separate step prior to executing your nice little chain? Or perhaps I need to learn more about externals?

While waiting for Marty, I'd like to add my two-cents.The following is a simplified description.

The original Unique Rectangle Types 1-6 were based on strong inferences/links internal to the UR pattern. Type 3 extended this to include subsets that could be formed with cells outside the UR pattern. Mike Barker found (and named) several other UR patterns using internal SLs and ALS patterns. Unfortunately, I find many of his descriptions difficult to follow. I must not be the only one because his UR names are seldom referenced. At one point, ronk started a thread to provide a better description of Mike Barker's URs, but he abandoned the project when there appeared to be little interest.

External SLs is a different approach. I don't know who started it, but I know that Ted wrote a detailed account here. Essentially, there must be at least one peer candidate that is true for a DP value in the UR. There are various ways of forming SLs using this information.

The following grid is from my notes on URs. It shows the companion cells where at least one peer candidate must be true for a DP value in the UR.

Code: Select all

/* 32 companion cells
 +-----------------------+
 | . . . | * * * | . . . |
 | * * * | X * X | * * * |
 | . . . | * * * | . . . |
 |-------+-------+-------|
 | . . . | * . * | . . . |
 | . . . | * . * | . . . |
 | . . . | * . * | . . . |
 |-------+-------+-------|
 | . . . | * * * | . . . |
 | * * * | X * X | * * * |
 | . . . | * * * | . . . |
 +-----------------------+
*/


So ...

In the grid for this puzzle, an internal SL on <4> using a Type 2 UR would eliminate <4> in r1c5. However, an external SL can also be formed between <5> and <8> in r1c5 as well. That's how Marty got around performing the Type 2 elimination as a separate step.

_

[Marty R.]

Marty

The type 2 UR (58), r78c36 leads to -4 r1c6 and r78c5. Is this not a separate step prior to executing your nice little chain? Or perhaps I need to learn more about externals?

Phil

Phil, I don't think I needed to do the Type 2. A player can choose to go with internals or externals and I chose the latter because it yields a short and sweet solution. I think Danny opined that that was a legitimate solution.

Take care,
Marty