## Another V Hard solved using T&E

Advanced methods and approaches for solving Sudoku puzzles

### Another V Hard solved using T&E

We have managed to solve this puzzle using Trial and Error, but my wife and I would rather use a new 'rule' to solve it more satisfactorily .

The story so far..........

274 **5 *3*
983 *** 5**
516 83* 7*4

325 **7 *6*
798 *5* 2*3
461 3** 975

85* *13 ***
632 *** 157
14* 5** 38*

If anyone out there has a (non T&E) 'rule' we would be eager to learn!!

Thanks
Guest

There is an X-wing of 1's but I'm not sure yet how far it brings you... (I'm still solving it)

Here are the possiblities for the number 1:

2 7 4 | 1? * 5 | * 3 1?
9 8 3 | 1? * 1? | 5 1? 1?
5 1 6 | 8 3 * | 7 * 4
-----------------------
3 2 5 | 1? * 7 | * 6 1?
7 9 8 | 1? 5 1? | 2 1? 3
4 6 1 | 3 * * | 9 7 5
-----------------------
8 5 * | * 1 3 | * * *
6 3 2 | * * * | 1 5 7
1 4 * | 5 * * | 3 8 *

As you can see there are only two possible locations for the number 1 in row 1 and only two in row 4 (r1c4, r1c9, r4c4 and r4c9). (the same is also true for column 6 and column 8)

This is called an X-wing, and it allows you to remove the 1 as a candidate from: r2c4, r2c9, and r5c4.

(If you don't immediatly see why: assume r1c9 does not have the numbe 1, then there is only one place where row 4 can have the number 1 (that is r4c4). If you would have the number 1 on another row in column 4, then r4c4 can't have the number 1, and this will lead to row 4 not having the number1)
Animator

Posts: 469
Joined: 08 April 2005

If you see the X-wing, then you should take a close look at the last column...

And when you are done with that, then you can fill something in in box 3 :)
Animator

Posts: 469
Joined: 08 April 2005

Thanks Animator for exposing our lack of rigour . We had found the x-wings of 1s, but failed to notice that it exposed a pair in column 9, etc. etc. Aaaaaaaaaaaaaaaaaagh..........

I guess thats the fascination of them, huh.
Guest