## Other use for "elimination" method

Post the puzzle or solving technique that's causing you trouble and someone will help

### Other use for "elimination" method

I was doing that elimination style because I was extremely stuck.

You know how you have a box that can be 1 of 2 answers, you "hypotheticallu" fill out a blank sheet to see what other boxes would be, if that box was option 1 or option 2, then you go through it looking for any boxes that share the exact same answer, whether it is option 1 or option 2. I call it elimination.

Well I think I discovered a new use for it. I was doing that method I just talked about, where I was filling it out, but I didn't get any matches. However, I had a 2AC option at bottom of a row (I am was doing Super Sudoku when I found this method), I was doing one of those option 1 or 2, and when I filled it out on separate paper, that 2AC box, had "2" for option 1, and "2A" for option 2.

I didn't solve it, but I realized that either way it can't be C! I don't know what method this is called, and I am sure this is a real thing, because I started doing the method in other hard sudkous and it always worked. I have a question about it.

1-What are these methods called? Because I have done like dozen of these, and seriously every time I get something like 2A or A for a 2AC box, like mentioned above, and I can always cross out the C. But I have a big question about this. In this same type of example, 100% of the time (as far as I have noticed since using it) the final answer always ends up being "A", aka the answer ends up being the one that is in the box for both option 1 and option 2. Like in another sudoku, I had a 3AB box, where I use my elimination from another box and either way this 3AB box ends up being 3 or 3B, which of course I can cross out A, but the final answer is 3, just like 2 was the answer for 2 or 2A.

However, I know this can be complete coincidence, but I am hoping this is a method, especially that one I just mentioned, I just haven't came across a sudoku where that didn't work. Like I have yet come across a box that is either 9 or 92, and it ends up being 2. It is always 9. I might come across one, but I am thinking this is a method.

Looking at a technique page online, the method I call "elimination", is called "forcing chains" according to another website. I am just wondering if the other uses of the method are called something different or just something you can do as part of it, but I am very interested if my theory of 92 or 2, theory is right, where the answer will always be the one that is on both option 1 and option 2.
RyanStorm

Posts: 32
Joined: 04 May 2014

### Re: Other use for "elimination" method

RyanStorm,

it would be nice, if you would come with an example (or you have to define, what you are talking about), so i can only guess, what you mean.

I suppose, with a box you mean, what we call a cell here (boxes for us are the 3x3 subgrids).
And what you call "answers" or "options", is probably, what we call candidates.

So if i understood it right, yes, i would call your methods (bivalue) cell forcing chains, as Sudoku Explainer uses them. However there are also some different definitions for forcing chains, e.g. the one in sudopedia seems to want a common number as outcome, and no common elimination. So in the sudopedia definitions probably "nice loop" is the equivalent technique - and in this forum (simple) AIC's (invaded from the Eureka forum). But though both are logically equivalent, they additionally have a strong emphasis on their notations.

Of course you are right, that if both "answers" imply, that another "box" does not contain an "option", you can eliminate it.

[Edit:]
At a second glance, it very depends on, what you are doing in your extra sheets, if the above techniques are equivalent.
If you don't follow a single chain from the choosen answer (A => B => C...), but solve them like having another puzzle, the equivalent would be a forcing net, or dynamic forcing chain (Sudoku Explainer), and would be hard to notate as nice loop or AIC.
You also have to think of situations like, that the chosen answer leads to a contradiction (contradiction chain) or the solution (what now ?).
So, as said, an example would help.
eleven

Posts: 1534
Joined: 10 February 2008