The New Sudoku Players' Forum

[pinhead1000]

For the life of me, I can't figure out how to solve any more of this particular puzzle.

1-X-9 X-X-2 X-4-X
4-2-X 1-5-X X-9-3
X-3-5 9-4-X X-2-1

8-5-1 2-7-4 3-6-9
3-7-2 6-1-9 4-5-8
9-4-6 5-8-3 2-1-7

X-X-4 X-2-1 9-3-X
2-1-X X-9-X X-X-4
X-9-X 4-X-X 1-X-2

[udosuk]

There are a naked pair and a naked triple, but they're not necessary...

An x-wing on 6 will do it...

(Keep an eye on row 2 and row 8, where must the 6 go? Can it go on the other rows along the corresponding columns?)

[keith]

There is an interesting pattern here called a "hinge", also known later as an "empty rectangle".

http://www.sudoku.org.uk/discus/messages/29/414.html?1135572720

http://forum.enjoysudoku.com/viewtopic.php?t=3251&start=0

Code: Select all

+----------------+----------------+----------------+
| 1#   68#  9#   | 378  36d  2    | 5678 4    56a  |
| 4#   2    78   | 1    5    678  | 678  9    3    |
| 67#  3    5    | 9    4    678  | 678  2    1    |
+----------------+----------------+----------------+
| 8    5    1    | 2    7    4    | 3    6    9    |
| 3    7    2    | 6    1    9    | 4    5    8    |
| 9    4    6    | 5    8    3    | 2    1    7    |
+----------------+----------------+----------------+
| 567c 68   4    | 78   2    1    | 9    3    56b  |
| 2    1    378  | 378  9    5678 | 5678 78   4    |
| 567f 9    378  | 4    36e  5678 | 1    78   2    |
+----------------+----------------+----------------+

The hinge is in Box 1; the possibilities for <6> lie only on one row and one column in the box.

Now, note the strong links in <6> labeled ab and de. Each has an end that lines up with the hinge cell, R1C1.

The first elimination, using ab, is: c cannot be <6>. Here is the reasoning:

If b is <6>, c is not <6>.

If b is not <6>, a is <6>, R3C1 is <6>, and c is not <6>.

Similarly, de can be used to eliminate <6> in cell f.

The rest of the solution is easy.

Keith

[udosuk]

What you described were equivalent to 2 separate instances of simple turbot fish...

Code: Select all

+----------------+----------------+----------------+
| 1   *68   9    | 378  36   2    | 5678 4   *56   |
| 4    2    78   | 1    5    678  | 678  9    3    |
|*67   3    5    | 9    4    678  | 678  2    1    |
+----------------+----------------+----------------+
| 8    5    1    | 2    7    4    | 3    6    9    |
| 3    7    2    | 6    1    9    | 4    5    8    |
| 9    4    6    | 5    8    3    | 2    1    7    |
+----------------+----------------+----------------+
|-567  68   4    | 78   2    1    | 9    3   *56   |
| 2    1    378  | 378  9    5678 | 5678 78   4    |
| 567  9    378  | 4    36   5678 | 1    78   2    |
+----------------+----------------+----------------+

+----------------+----------------+----------------+
| 1   *68   9    | 378 *36   2    | 5678 4    56   |
| 4    2    78   | 1    5    678  | 678  9    3    |
|*67   3    5    | 9    4    678  | 678  2    1    |
+----------------+----------------+----------------+
| 8    5    1    | 2    7    4    | 3    6    9    |
| 3    7    2    | 6    1    9    | 4    5    8    |
| 9    4    6    | 5    8    3    | 2    1    7    |
+----------------+----------------+----------------+
| 567  68   4    | 78   2    1    | 9    3    56   |
| 2    1    378  | 378  9    5678 | 5678 78   4    |
|-567  9    378  | 4   *36   5678 | 1    78   2    |
+----------------+----------------+----------------+

[pinhead1000]

There are a naked pair and a naked triple, but they're not necessary...

An x-wing on 6 will do it...

(Keep an eye on row 2 and row 8, where must the 6 go? Can it go on the other rows along the corresponding columns?)

Wow! Perfect. That was the key to the whole thing. And your clue was perfectly worded, too.

Hopefully I can do the next "Very Hard" one by myself...