dailysudoku.com

[Earl]

Since todays VH was not VH I found another one,
which was VH. Anyone see a next step?

Thanks

Earl

[keith]

Take a look where <7> goes in Box 9, then in Box 4.

Keith

[jLo]

Don't know if this is the path of least resistance, but here's
how I approached this one.

After doing the box-line reductions on <7>s in box 7 and box 4
you end up here.

[Earl]

jLo,

Your final major step might be somewhat simplified.
Regardless of whether R1C9 is 1 or 2,
2 is eliminated from R8C5 which then must be 7.

Thanks for all your work.

Earl

[jLo]

[Earl]

jLo,

I saw it only as an alternative to your last major step, i.e. assuming the fifth grid you posted. If R1C9 is 1 the X-wing holds and R8C5 cannot be 2. If R1C9 is 2 R8C8 is 2 by hard pairs and R8C5 cannot be 2.

I might have done something wrong, but that is how I see it. I am still learning these techniques.

Thanks

Earl

[jLo]

[Asellus]

Earl,

Technically, it seems to me that that qualifies as a finned X-Wing since the 2 at R8C5 is eliminated either by the X-Wing or by the fin (R1C9) via the coloring on 2.

We normally think of fins only as cells that provide a direct alternate elimination to that of the X-Wing (or other fish). This example shows that the fin elimination can be mediated by an intervening technique. (An Empty Rectangle might provide a similar opportunity, for instance.)

Worth keeping in mind!

PS: I was able to solve this puzzle without recourse to the UR or to what-ifs. However, it required quite a number of steps (some very interesting). I may work on it some more later to see if I can streamline it. If so, maybe I'll post the steps.

[Asellus]

jLo,

In your 17 UR, I believe it falls into one of the defined "Type" categories. (Type 6 maybe? I'm terrible at remembering the Type numbers!) It is the type where one side of the UR is part of an ALS. In this case, the ALS comprises R169C9, {1247} in 3 cells. The "external" cell(s), R1C9 in this case, does not contain <7>. Thus, <1> can be eliminated from R69C9.

The rule does not allow the elimination of <7> from R9C9. But, I suspect that that follows quickly.

[Asellus]

Okay... here it is, another way to the solution without using the 17 UR (as tempting as it may be) and without any novel what-ifs. I tried to streamline it, but it didn't cooperate very much. No doubt someone out there will see a shortcut that eludes me. Nevertheless, there is some interesting scenery along my chosen path. I can't argue that it is a "better path." It's just different.

Starting just after jLo's <1> Coloring, but before the UR argument, I extended the Coloring further to eliminate <1> from R6C5. We are now ready for a Color Wing on <2>:

[Mogulmeister]

Did anyone spot this early possibility right at the start of Earl's puzzle ?

Notice that as well as the strong links elimination on <1> that jLo pointed out earlier, we can use the same structure to eliminate <2> as well.

What am I saying ? Simply put, that same structure pictured below eliminates both 1 and 2 from r8c5 which then turns the puzzle to toast.

[Edit to replace lost image due to TinyPic demise]

[jLo]

[Mogulmeister]

Yes jLo - this works because of the preponderance of bivalues. If we look at the polarity on 1's we are saying "1" or "not 1". In many cases "not 1" means 2.

Let us assume that green is "not 2" ie 1

If you look in box 2 you will notice that a triple <289> is forced, making box 2 column 5 contain 2. Or if you prefer, the 2 (or not 1) in r3c8 eliminates the 2's in r3 in box 2.

Effectively this structure will have an eliminating 2 and an eliminating 1 whatever the polarity.

[jLo]

[Asellus]

I certainly didn't see that <2> elimination. Nice!

It is analogous to the Finned X-Wing discussed above: a technique extended using color wrapping. In this case, it is ALS, {1289}{12}, extended by color wrapping.

In the first case, I wouldn't have recognized the pattern as a possible Finned X-Wing based elimination. And in the second case, I would have neglected the ALS because it doesn't provide any "direct" candidates for elimination.

I think it may take some time before I am able to "see" such possibilities as these, though!

[Mogulmeister]

I always think it is useful when studying puzzles to see what builds upon an apparently simple strong links pattern. I saw here that there were a good many bivalues which always arouses interest eg think about the xy chains that often have multiple eliminations.

[TKiel]

That was an excellent catch on the 2 but I disagree with your statement "that same structure pictured below eliminates both 1 and 2..." The 1 is pretty obvious, since it's simple coloring (strong links) but in the case of the 2 the structure shown (highlighted) can in no possible way, by itself, eliminate the 2 at r8c5.

[Mogulmeister]

We are talking about that structure - I was not setting forth a generalised proof- the statement with respect to that puzzle is absolutely correct.

[Asellus]

I can see Tracy's point in that at least a couple of us couldn't see how that <2> was eliminated until the reply to jLo mentioning the potential locked set. However, I think that's perfectly fine. None of us can be sure something we post will be immediately clear to others. That's the value of a discussion board: things become clear through the back-and-forth dialog.

[TKiel]