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Question about a solving technique
#1
Hi all,

I am working on a puzzle (sudoku) which ends in a situation where all cells are filled in except these:

 x  x  x  ab x  abc ac  x  x
 x  x  x  x  x  ac  ac  x  x
 x  x  x  x  x  x   x   x  x
 x  x  x  x  x  x   x   x  x
 x  x  x  x  x  x   x   x  x
 x  x  x  x  x  x   x   x  x
 x  x  x  x  x  x   x   x  x
 x  x  x  ab x  ab  x   x  x
 x  x  x  x  x  x   x   x  x

The X's are not important. Only the 7 cells with candidates abc in them are.


As I have blundered with this before, I thought I'd just ask here: is this an ok BUG that allows the solver to deduct that R2C6 cannot be a c (because otherwise you would end up with two solutions)?

Thanks in advance,


SirWoezel
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#2
If by "working" you mean "solving", and you don't care about proving that there's only one solution, then R1C6 must be "c" (and it follows that R2C6 is not "c").

If by "working" you mean "constructing", then you'll need something else (e.g. a variant rule) to resolve these cells, or else the puzzle has multiple solutions.
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#3
Thank you Rob, but doesn’t this -essentially- mean that a BUG can never be a valid solving technique?

Point being: I know this technique exists, but I have trouble understanding it. To me my puzzle simply has three solutions. r1C6 is either a, b or c and they lead to a different end-grid. But then, why does the technique exist at all?
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#4
Come to think of it: the same thing goes for ‘unique rectangles’. Is it a valid technique or just a ‘lazy way’ of forcing a unique solution that basically is not there?
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#5
What is a "technique"? Is it the same as a "solving technique"? What does it mean for a technique to be "valid"?
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#6
I think that all uniqueness techniques require the puzzle to be unique in the first place, which yours is not. Even if you stated the uniqueness in the puzzle description, this would be a lie, since the puzzle does definitely have 3 solutions.
What could be stated is something along the lines of: At some point on the solving path you will have to make a choice for a cell that leads to a unique solution after that choice is made and all other choices don't lead to a unique solution after the choice is made.
But that does not make the puzzle unique and it is questionable if said choice for the cell is in any way better than the others. It is just the first uniqueness related joice to be made in a particular solution path that avoids making further uniqueness related choices.

In the interest of keeping mental sanity it s probably advisable to think in this way:
Every unique sudoku can be solved by other means (which in the case of BUG are typically XY-chains, but in the extreme case might just be brute force) and uniqueness techniques may provide shortcuts to that one solution.
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#7
@slowLarry
Wow, now that is exactly the answer I was looking for. Just the first 14 words made it perfectly clear. You've actually opened my eyes...
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#8
Think of it as a shortcut to the solution which is unique, but you can't see how to prove it yet. For this, it has to be unique by other means and your example is not complex enough for that. Your "x" digits are not irrelevant, they are needed to "enforce" a unique solution from outside the marked cells.

Andrew Stuarts Sudoku solver usually has detailed examples on the description pages and a discussion section that might lead to other examples or sources.

https://www.sudokuwiki.org/BUG
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#9
Uniqueness techniques are useful in competitions, but a puzzle that absolutely requires uniqueness techniques to solve is generally considered faulty.
Das Schönste an der deutschen Sprache ist die Onomatopoesie: blubbern, prasseln, watscheln, klirren.
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#10
Ein Rätsel eindeutig zu machen kann aber auch zur Aufgabe gehören. Da war neulich im Portal so ein "Schwärzen Sie einige Kreise so, daß ein eindeutige lösbares Masyu entsteht".
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