- Code: Select all
`4 . . | 2 . . | 1 . .`

. . 6 | . . 4 | . . .

7 . . | 8 5 . | . . .

-------+-------+------

2 5 . | 4 . . | . . 1

. . . | . . . | . . .

8 . . | . . 3 | . 9 7

-------+-------+------

. . . | . 7 9 | . . 3

. . . | 1 . . | 6 . .

. . 8 | . . 2 | . . 4

Standard techniques take us to:

- Code: Select all
`4 3|8|9 3|5 | 2 3|9 6 | 1 7 5|8`

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

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

------------------------------+------------+---------------------

2 5 9 | 4 8 7 | 3 6 1

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

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

------------------------------+------------+---------------------

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

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

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

The cells {r1c2,r2c2,r3c2} must contain three of the five values {1,2,3,8,9}. Now, the set can't contain 2 and 3, or we wouldn't be able to fill r3c3. Similarly, the set can't contain 1 and 9, or we wouldn't be able to fill r9c2. Therefore, the three cells must contain an 8, one of {2,3} and one of {1,9}. Critically, this means that the values {2,3} in Box 1 and the values {1,9} in Column 2 are accounted for, so we're in a position to make lots of eliminations - 3 from r1c3 (gives us a 5), 3 from r2c1, 1 from r6c2 (gives us a 4) and 1 from r7c2. Magic! Even better, there are similar constructions elsewhere. Note {r2c7,r2c8,r2c9} contains three of {2,3,5,8,9}, with the other values in r1c9 and r2c5 and that {r7c1,r7c2,r7c3} contains three of {1,3,5,6,9} with the other three values in r5c1 and r9c2, so we eliminate r2c1=9, r2c2=3, r2c2=9 and r7c3=1. Sudoku carnage!

I'll write at greater length tomorrow but in the meantime try the following puzzles, which, if you've understood the above, you should be able to solve without recourse to forced chains:

- Code: Select all
`. 8 . | . 2 . | . . .`

1 . . | 7 . . | 6 . .

. . 3 | . . 5 | . . .

-------+-------+------

8 . . | 9 . . | 1 . 2

. 7 . | . . . | . 3 .

4 . 5 | . . 6 | . . 7

-------+-------+------

. . . | 1 . . | 5 . .

. . 9 | . . 4 | . . 8

. . . | . 3 . | . 7 .

. . . | 2 . . | . 5 .

. . . | 4 . 9 | . . 6

. . 7 | . . . | 4 . 1

-------+-------+------

8 . . | . . 7 | 2 . .

. 3 . | . . . | . 9 .

. . 9 | 6 . . | . . 7

-------+-------+------

4 . 2 | . . . | 3 . .

6 . . | 8 . 5 | . . .

. 9 . | . . 1 | . . .