Larrysez wrote:I cannot for the life of me see any way to solve this puzzle other than by just taking a wild guess about one of the remaining unsolved squares and seeing whether it works out or not. This happens once in a while. Is there some technique I could use?
The answer to your question about a technique you can use is yes, but I'm not going to elaborate on that now. (you might look at my other posts on the forum that come later).
For this particular puzzle above, you don't need
"possibility matrices", "locked candidates" or any other convoluted *!#$.
This is row8
48_  593  _6_ This is colH

6
4
___
9

2
___
1
8
5row8 needs a 7 somewhere.
7 cannot go beside 8, because 7 at C3 blocks.
Therefore the 7 must come to the left or the right of 6.
Erase your pencil marks there and put "m7,6,m7"
Your two m7's indicate that 7 must come to the left or right of 6, and nowhere else in that box.
The presence of two m7's here means there is an "implied 7" in that box now.
In particular, your implied 7 is off the middle column.
Can we utilize this fact?
Yes.
colH needs a 7. Where could that go? It cannot go above the six because it is blocked by your m7s.
Therefore it must go in the other available slot. (It
must go there).
colH is now fleshed out. 3 is the only remaining digit. It must go in the top.
3
6
4
___
9
7
2
___
1
8
5