## ALS-Complementary Pair Example

Everything about Sudoku that doesn't fit in one of the other sections

### ALS-Complementary Pair Example

This example illustrates 2 complementary pair solving techniques. I used a 3 W-wing to eliminate 3 from r1c9 and reach this point in the puzzle. The complementary pair is r1c4 and r6c6, i.e. both cells must be either 1 or 8. Note the 168 ALS in r16c9. The ALS-complementary pair rule can be stated as follows. If each cell of an xy complementary pair sees one celll of an xyz ALS then z can be eliminated from any cell that sees all z's in the ALS. In this puzzle Z=6 is eliminated from r8c9. Next note the 8 xy-wing with pivot at r5c7. If the pincer cells r4c8 and r5c3 are combined with the conjugate pair r46c6 it becomes an 8 z-color wing which removes 8 from r6c3. This makes r16c9 a conjugate pair and sets up the other complementary pair technique which can be staed as follows. If each cell of a complementary pair xy sees one cell of a conjugate pair x, rhen both complementaty pair cells are y. This makes r1c4=r6c6=1 and solves the puzzle.

ALS-Complementary Pair Example
Code: Select all
` |-----------------+-----------------+-----------------| |   2    9    7   |  18    5    4   |  36  1368  68   | |   4    8    6   |   2    3   17   |   9    17   5   | |   5    3    1   |  78    9    6   |   4    78   2   | |-----------------+-----------------+-----------------| |   9    1   25   |   6    4   38   |  25   38    7   | |   6    7  -58   | 135    2    9   |  35    4  13-8  | |   3    4  25-8  |  15    7   18   | 256    9  168   | |-----------------+-----------------+-----------------| |   7    6    3   |   9    8    2   |   1    5    4   | |   8    2    9   |   4    1    5   |   7   36  3-6   | |   1    5    4   |  37    6   37   |   8    2    9   | |-----------------+-----------------+-----------------| `

The original puzzle is Sudoku Expert Book 38 #5
Last edited by Bud on Mon Feb 16, 2009 1:47 am, edited 2 times in total.
Bud

Posts: 56
Joined: 24 August 2008

### Re: ALS-Complementary Pair Example

Bud, your posted puzzle has no solution.

Bud wrote:This example illustrates 2 complementary pair solving techniques. .... The complementary pair is r1c4 and r6c6, i.e. both cells must be either 1 or 8.

I've seen other people use the complementary term too, but have you ever wondered ... how is the pair complementary?
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### ALS-Complementary Pair Example

Hi Ron,

I added the puzzle # to the post and corrected errors in the grid in box 9. Sorry about that.
I don't like the term "complementary" either. I got it from Keith at DailySudoku.com. To me complement mena inverse. Do you have a better name for it?

Here is the original puzzle:

007 054 000
006 000 900
000 000 000
910 600 000
000 020 040
300 000 000
060 900 100
800 000 000
004 000 020
Bud

Posts: 56
Joined: 24 August 2008