## Solving Puzzles Using Triangles

Advanced methods and approaches for solving Sudoku puzzles

### Solving Puzzles Using Triangles

Okay, so I've seen this as a logical possibility in my mind, yet I as of yet still cannot wrap my mind around the intricacies of it. I have noticed that each number within a given row forms a triangle through the three columns, and the three triangles may also be related to each other in some sort of fashion, which I also have not been able to pinpoint.

I admit that this may have already been discussed, but after clicking on a couple of threads I realize that while I may be doing well, not beginning Calculus has rendered me totally incapable of understanding some of the things discussed here.

I have some raw data from a puzzle that I did, where the first number corresponds to the x value of the block that said number is in, and the second corresponds to the y value, with each block having values 1-3 for x and y.

1: 23 , 22 , 32
33 , 32 , 21
12 , 23 , 11
2: 21 , 32 , 13
13 . 21 . 22
31 . 12 . 33
3: 33 , 22 , 31
11 , 12 , 13
22 , 31 , 23
4: 32 , 33 , 11
23 , 11 , 32
13 , 22 , 21
5: 11 , 13 , 12
32 , 23 , 21
23 , 32 , 31
6: 13 , 21 , 22
31 , 13 , 12
21 , 33 , 32
7: 22 , 31 , 33
32 , 23 , 11
11 , 13 , 22
8: 12 , 23 , 21
22 , 33 , 31
32 , 11 , 13
9: 31 , 12 , 23
12 , 31 , 33
23 , 21 , 12

I'm not looking for the obvious patterns (that all the x coordinates in the first blocks of the puzzle have 1, 2, and 3 only once, and that all the y coordinates in the blocks in a given row of the puzzle have 1, 2, and 3 only once).

If you think that what I'm talking about is impossible or worse, don't be afraid to tell me so - it wouldn't be the first time my mind has played tricks on me.
bandnerd37

Posts: 1
Joined: 27 December 2007

I'm not sure I understand your nomenclature, for example, I would have thought your first row would read 1:23,11,32 so this may not be helpful. It sounds like what you are referring to is also known as braid analysis or traveling pairs/triples. Check Condor's thread (and included links) and see if they are related.
Mike Barker

Posts: 458
Joined: 22 January 2006