Isolated Subpuzzles and Local Uniqueness

Advanced methods and approaches for solving Sudoku puzzles

Postby RW » Fri Nov 14, 2008 6:51 am

denis_berthier wrote:
RW wrote:Other techniques define ways of spotting contradictions. Uniqueness technique defines new contradictions.

In all the cases, you have to define the patterns that lead to contradictions and then you have to spot these patterns.

My view on uniqueness technique is a bit different. To me uniqueness technique is only about defining new contradictions. In an unique sudoku, a completed unavoidable set with no given clues or a deadly pattern with no extra candidates is a contradiction that leads to 0 solutions. Exactly like a unit missing a candidate or a cell with no candidates is a contradiction that leads to 0 solutions. I don't need to define new patterns that lead to uniqueness contradictions, I can use the same patterns I use to find regular contradictions. Therefore the whole term "uniqueness technique" is a bit misleading, because there is essentially no new technique involved, only new contradictions.

It's probably true that there are more rules for uniqueness, but they may also be so specific that trying to use them all would be very counter productive.

Exactly. In terms of efficiensy, it's best to use some generalised rules that defines the most common unavoidable sets and deadly patterns. With a few rules you can cover quite a lot of common patterns. Then there will always be a lot of strange exotic patterns that most likely will never appear in a puzzle, but if they did, they would allow some eliminations. Like this technique...

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Postby Allan Barker » Fri Nov 14, 2008 4:46 pm

RW wrote:
denis_berthier wrote:
RW wrote:Other techniques define ways of spotting contradictions. Uniqueness technique defines new contradictions.

In all the cases, you have to define the patterns that lead to contradictions and then you have to spot these patterns.

My view on uniqueness technique is a bit different. To me uniqueness technique is only about defining new contradictions.


I noticed in some of SteveK's solutions, he would take a potential UR and derive from it a strong (inferred) inference, on which he would build the rest of his solution. The solutions looked like any other except for a rectangle (the UR) stuck at the end.

I found I could adapt this to my standard Sudoku logic solver by allowing a user to manually enter an inferred inference that is then used by the solver like any other of the original 324 sets. This simply expands the game to 325 sets. This seems to work but the user must spot and enter the inferred inference. Of course, he/she must know the puzzle has a unique solution. (Actually, I think this is not true, the user must only know that the chosen UR is not part of a multiple solution region.)

My question is, as a newbie to uniqueness, given a puzzle with a unique solution, I can use any potential UR in the puzzle assuming that it produces some useful inference, right? I.e., there are no other special requirments of the local environment. Of course, I must search for the URs.

Denis, I think you could do the same. In fact, nrczt-braids might be the ideal way since they allow one to pick and choose desired logical sub-components.

PS. I use the term nrctz-braids to distinguish them from DPB's braids and braiding analysis.
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Postby denis_berthier » Fri Nov 14, 2008 7:36 pm

Allan Barker wrote:Denis, I think you could do the same. In fact, nrczt-braids might be the ideal way since they allow one to pick and choose desired logical sub-components.

Vocabulary:
nrczt-braids are the basic zt-braids(ECP+NS+HS)
For other families FP of generating patterns, I use the name zt-braids(FP)

Of course a family FP of patterns could contain patterns for UR1 or similar U-rules.

But, given that zt-braids(FP) can be shown to solve all the known puzzles for very simple families FP, with no uniqueness hypothesis, I can see no reason to make such an assumption and to use such patterns.
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Postby RW » Fri Nov 14, 2008 10:03 pm

Allan Barker wrote:
RW wrote:
denis_berthier wrote:
RW wrote:Other techniques define ways of spotting contradictions. Uniqueness technique defines new contradictions.

In all the cases, you have to define the patterns that lead to contradictions and then you have to spot these patterns.

My view on uniqueness technique is a bit different. To me uniqueness technique is only about defining new contradictions.


I noticed in some of SteveK's solutions, he would take a potential UR and derive from it a strong (inferred) inference, on which he would build the rest of his solution. The solutions looked like any other except for a rectangle (the UR) stuck at the end.

Yes, this is a good way of using uniqueness technique. Though the rectangle doesn't necessarily have to be at the end, it can be in the middle as well. Uniqueness contradictions may be used to create inference, just like we use regular contradictions to create inference.

But still, the knowledge of deadly patterns as such doesn't give us any eliminations. We need to know techniques that make something out of the inference we see in the grid. These techniques are the same for uniqueness eliminations and regular eliminations.

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