Technic 3: Opposition

Technic 3: Opposition


This technic lets you eliminate one candidate.


If a cell has n candidates and n neighboring cells pertaining to an another and same region and the neighboring cells have the same candidates than the original cell. If only one another cell (the resulting cell) exists in this region that is not a neighbourg of the original cell and this cell has all the candidates of the original cell plus an extra candidate. Then we could eliminate this extra candidate in this resulting cell.. 


The neighboring cells of the original cell, have all the candidates of the original cell. So its means that if the original cell elects one of its candidates then the neighboring cells will eliminate this candidate and the resulting cell will have this candidate because this is the only other cell having the candidate in the region. At the end this resulting cell will have only the candidate of the original cell. So we could eliminate all the other caniddates in the resulting cell.


This is why I call this technic opposition because ultimely the candidate elected inf the original cell will be in the resulting cell..



From the Suguru at the figure 3.1 with the basic technics we arrive at this situation (fig 3.2).

To be able to progress you need to apply the opposition. The original cell c3 has two candidates: 1 and 3 and also two neighboring cells C2 and B4. These two neighboring cells have together the same candidates that the original cell ( 1 and 3  and even one more 4, but we don't care). In this same region it have only one other cell C1 having the same candidates than the original cell (1,3) and also an extra candidate 2.  It is very important to notice that this cell is the only other cell with the neighboring cell C2 and B4 that have the canidates of the original cell. So based on the rule we could eliminate the extra candidate 2 from C1.


If the original cell C3 finaly has a 3 then C1 and B4 will eliminate this candidate and C1 will have a 3. And if C3 has 1 then C2 will eliminate the candidate 1 and C1 will have the 1. So in any case C1 will never have the 2. This is why we could eliminate it.  The cells C3 and C1 are in opposition. 


With that you could find the solution (fig 3.3).

You could try by yourself with this puzzle Suguru Opposition.pdf.