The New Sudoku Players' Forum

[bingham]

This one appeared originally in the forum under something like "advanced techniques", but I cannot now find the original
1 6 - ! - 7 - ! 5 - -
- - - ! - - 1 ! - 6 -
- 4 - ! 5 6 - ! 3 1 -
---------------------
- 1 2 ! - - - ! 6 - -
- - - ! - - - ! 1 - 3
- - 9 ! - - - ! 4 2 -
---------------------
- 8 1 ! - 4 - ! 7 3 -
- 5 - ! 7 - - ! - - -
- - 6 ! - 3 8 ! - - -

Fairly straightforward logic led to

1 6 38 ! 23489 7 2349 ! 5 489 2489
35 29 357 ! 34 289 1 ! 289 6 47
29 4 78 ! 5 6 29 ! 3 1 78
----------------------------------------------------
458 1 2 | 3489 589 349 | 6 7 589
4568 7 458 | 24689 2589 249 | 1 589 3
568 3 9 | 68 1 7 | 4 2 58
-----------------------------------------------------
29 8 1 | 29 4 5 | 7 3 6
34 5 34 | 7 29 6 | 289 89 1
7 29 6 |1 3 8 | 29 45 45

I have solved it (several times) using different starting points for a T&E, but every solution has required a long (>15 cells) path leading to a dead end.
Any clues please?

[wintder]

Code: Select all

1 6 .|. 7 .|5 . .
. . .|. . 1|. 6 .
. 4 .|5 6 .|3 1 .
-----+-----+-----
. 1 2|. . .|6 . .
. . .|. . .|1 . 3
. . 9|. . .|4 2 .
-----+-----+-----
. 8 1|. 4 .|7 3 .
. 5 .|7 . .|. . .
. . 6|. 3 8|. . .

Too hard for me.

[Sped]

Code: Select all

 *-----------*
 |16.|.7.|5..|
 |...|..1|.6.|
 |.4.|56.|31.|
 |---+---+---|
 |.12|...|6..|
 |...|...|1.3|
 |..9|...|42.|
 |---+---+---|
 |.81|.4.|73.|
 |.5.|7..|...|
 |..6|.38|...|
 *-----------*


After (not quite so) simple steps we arrive here:

Code: Select all

 
 *--------------------------------------------------*
 | 1    6    38^  | 348  7    349  | 5    49   2    |
 | 35*  29   357  | 34   289  1    | 89   6    47   |
 | 29   4    78^  | 5    6    29   | 3    1    78^  |
 |----------------+----------------+----------------|
 | 48   1    2    | 348  5    34   | 6    7    9    |
 | 6    7    45   | 29   89   249  | 1    58   3    |
 |(5)8  3    9    | 6    1    7    | 4    2    58*  |
 |----------------+----------------+----------------|
 | 29   8    1    | 29   4    5    | 7    3    6    |
 | 34   5    34   | 7    29   6    | 289  89   1    |
 | 7    29   6    | 1    3    8    | 29   45   45   |
 *--------------------------------------------------*


The xy chain:

5-(r2c1)-3-(r1c3)-8-(r3c3)-7-(r3c9)-8-(r6c9)-5

eliminates the 5 in r6c1, reducing it to singles.

As a nice loop:

[r6c1]-5-[r2c1]-3-[r1c3]-8-[r3c3]-7-[r3c9]-8-[r6c9]-5-[r6c1], => r6c1<>5

[Carcul]

Code: Select all

 *----------------------------------------------------------*
 | 1      6      38  | 3489   7      349 | 5      489    2  |
 | 35     29     357 | 34     289    1   | 89     6      47 |
 | 29     4      78  | 5      6      29  | 3      1      78 |
 |-------------------+-------------------+------------------|
 | 458    1      2   | 348    58     34  | 6      7      9  |
 | 4568   7      45  | 24689  2589   249 | 1      58     3  |
 | 568    3      9   | 68     1      7   | 4      2      58 |
 |-------------------+-------------------+------------------|
 | 29     8      1   | 29     4      5   | 7      3      6  |
 | 34     5      34  | 7      29     6   | 289    89     1  |
 | 7      29     6   | 1      3      8   | 29     45     45 |
 *----------------------------------------------------------*


[r3c9]=8=[r6c9]=5=[r6c1]-5-[r2c1]=5=[r2c3]=7=[r2c9]-7-[r3c9],

=> r3c9<>7 and the puzzle is solved.

The ATILA in cells [r3c16|r5c56|r7c14|r8c5], together with cells r4c5, and r5c38 also allows the immediate deductions: r5c14<>4,5,8.

[bingham]

Thank you Sped and Carcul. Both approaches are much more elegant than looong paths with dead ends!
Have you another puzzle of comparable difficulty that I can use to see whether I've kicked the habit?
Bingham

[ncantoral]

coloring on 9 does some interesting things.

I also found a 68 UR and a 34 UR