The New Sudoku Players' Forum

[hrcjcr]

Maybe I'm missing a chain or wing because my eyes just aren't focusing anymore. T&E got me a correct solution, but was hoping for a better way of solving this.
What I have so far:


5 26 8 12 1236 9 7 13 4
479 249 234 12457 12357 147 6 1359 8
479 1 346 8 3567 467 39 359 2
6 3 7 19 19 2 8 4 5
8 29 12 6 4 5 19 7 3
49 5 14 3 78 78 2 6 19
1 467 46 2579 25679 3 45 8 69
3 4678 9 157 15678 1678 45 2 16
2 68 5 4 1689 168 139 39 7

Any help would be appreciated.
jcr[code][/code]

[Shazbot]

The 4 in r9c4 would exclude 4 as a candidate from r2c4. This is a little easier to follow:

Code: Select all

 *-----------*
 |5.8|..9|7.4|
 |...|...|6.8|
 |.1.|8..|..2|
 |---+---+---|
 |637|..2|845|
 |8..|645|.73|
 |.5.|3..|26.|
 |---+---+---|
 |1..|..3|.8.|
 |3.9|...|.2.|
 |2.5|4..|..7|
 *-----------*

 
 *--------------------------------------------------------------------*
 | 5      26     8      | 12     1236   9      | 7      13     4      |
 | 479    249    234    | 1257   12357  147    | 6      1359   8      |
 | 479    1      346    | 8      3567   467    | 39     359    2      |
 |----------------------+----------------------+----------------------|
 | 6      3      7      | 19     19     2      | 8      4      5      |
 | 8      29     12     | 6      4      5      | 19     7      3      |
 | 49     5      14     | 3      78     78     | 2      6      19     |
 |----------------------+----------------------+----------------------|
 | 1      467    46     | 2579   25679  3      | 45     8      69     |
 | 3      4678   9      | 157    15678  1678   | 45     2      16     |
 | 2      68     5      | 4      1689   168    | 139    39     7      |
 *--------------------------------------------------------------------*


From there, Simple Sudoku uses colours to exclude 6 from r7c5, then multiple colours to exclude 6 from r8c5. Then no more hints available. Too advanced for me. Sorry.

[tso]

Two xy-type forcing chains will solve this puzzle:

r6c3=4 => r2c3<>4 and r3c3<>4
r6c3=1 => r6c9=9 => r7c9=6 => r7c3=4 => r2c3<>4 and r3c3<>4
Therefore, r2c3<>4 and r3c3<>4

Then,

r2c3=3 => r3c3=6
r2c3=2 => r5c3=1 => r5c7=9 => r3c7=3 => r3c3=6
Therefore, r3c3=6

The rest can be filled with singles alone.

[hrcjcr]

I started if/thens with r1c2. Choosing a 6 causes a contradiction 8 steps later. Using a 2 basically solves it.
What prompted you to look at r6c3, or did you start elsewhere first?

[tso]

What prompted you to look at r6c3, or did you start elsewhere first?

I started elsewhere, but this was the first usefull thing I noticed. I didn't physically draw labled edges -- if I hadn't found these, that would have been my next step.

I looked for short 'nice loops' -- either non-repetitive or repetitive.

The cells r67c39 is a 4 cell non-repetitive nice loop -- if you label the edges between the four cells, there is no repetition -- 1, 9, 6, 4. Therefore,

Exactly one of r6c39 must be a 1.
Exactly one of r67c9 must be a 9.
Exactly one of r7c39 must be a 6.
Exactly one of r67c3 must be a 4.

This allows you to eliminate '4' from both r23c3 as well as '6' from r7c2.


I looked for the second chain starting with the cells that had been reduced for no good reason and found a repetitive loop by eye without following any strict series of steps. Again, if I hadn't seen this quickly, I would have drawn labeled edges.

[hrcjcr]

Thanks,
jcr