## Why my guesses are always wrong

Advanced methods and approaches for solving Sudoku puzzles

### Why my guesses are always wrong

I noticed that whenever I had to resort to trial and error or to set up a forcing chain in the bilocation/bivalue graphs so far I ALWAYS chose the wrong number when there was a binary choice, with only one exception (out of a dozen guesses).

First I thought "bad luck!", a couple of puzzles later "Murphy's Law!", but now I tend to think that this is a systematic effect, even though the "statistics" is not overwhelming...

I don't mean to imply that there is some systematics in a 50:50 effect - of course there is none! But I believe that the choice in reality is not 50:50.

Let me explain why: I do not choose at random, but rather I take the number which "stands out a mile"; so far there always has been a unique choice, because one of the two numbers typically collapses more cells than the other - one of the two choices typically is more "rigid", in the sense that it has stronger implications on other cells in the sudoku.

And this is probably the reason why this number leads to a contradiction: BECAUSE it has stronger implications on the remaining cells in the sudoku.

Of course, this will not always be the case, nor is this anything resembling a "proof" that this will always work that way, but it seems plausible enough to me to explain why most of the time the "convenient" choice leads to a contradiction.

Has anybody made similar experiences with guessing/choosing the initial number for a forcing chain?
Big Blue

Posts: 28
Joined: 01 August 2005

Why would you have to guess any number after you have the bilocation/bivalue graph plotted. It is a matter of picking a nice cycle to use.
Jeff

Posts: 708
Joined: 01 August 2005

Well, because unfortunately not all difficult puzzles allow a straightforward application of bilocation methods - conflicting paths etc.

In these cases the bilocation graph is still a very useful tool, IMHO, to set up some chain which eventually leads to contradiction - you can often see where the "critical cells" are and then insert there an educated guess.
Big Blue

Posts: 28
Joined: 01 August 2005

Plot the complete bilocation/bivalue graph so that you don't have to guess at all. And then following these rules to find the nice cycles.

1) Bilocation edges are strong links.
2) Bivalue edges can be strong or weak links.
3) A strong link can be used as a weak link, but not the other way around.

4) To propagate from strong link to strong link, label must change value except for the repetitive cycle at the cell of inclusion only; no restriction on the number of candidates in the node.

5) To propagate from weak link to weak link, label must change value except for the repetitive cycle at the cell of exclusion only; the node must be 'bivalue'.

6) To propagate from strong link to weak link or vice versa, the label must be same; no restriction on the number of candidates in the node.

7) Rules for candidate inclusion and exclusion are basically same as those for repetitive cycle and non-repetitive cycle.

The only price to pay for a logical solution is just TIME, because it's time consuming. In return, it's full satisfaction.
Jeff

Posts: 708
Joined: 01 August 2005