A Hitch-hikers Guide to Uniqueness-based Solving Techniques

Advanced methods and approaches for solving Sudoku puzzles

Postby ravel » Fri Oct 05, 2007 8:09 pm

coloin wrote:[I dont know how you can say they are easy to spot !
Most 2-digit BUG-light unavoidables are rather easy to spot, because you just can "extend" them with simple rules. E.g when you have this one in mind
Code: Select all
+----------+----------+
|  .  12 . |  12 .  . |
|  .  .  . |  .  .  . |
|  .  12 . |  12 .  . |
+----------+----------+
but the puzzle shows you
Code: Select all
+----------+----------+
|  .  12 . |  12 .  . |
|  .  .  . |  .  .  . |
|  .  12 . |  .  .  12|
+----------+----------+
you can go "around the corner" and look, if there is a "stopper" there like
Code: Select all
+----------+----------+----------+
|  .  12 . |  12 .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  12|  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  12 .  12|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
or one more corner
Code: Select all
+----------+----------+----------+
|  .  12 . |  12 .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  12|  .  .  . |
+----------+----------+----------+
|  .  .  . |  12 .  . | 12  .  . |
|  .  .  . |  .  .  12| 12  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
the second variant is
Code: Select all
+----------+----------+----------+
|  .  12 . |  . 12  . |  .  .  . |
|  .  12 . |  .  .  . |  . 12  . |
|  .  .  . |  . 12  . |  . 12  . |
+----------+----------+----------+
All these combinations are easy to spot in a candidate grid, when you dont have much extra candidates

Also with 3 digits and pairs of candidates (i.e 2 possible solutions) some extensions are easy, when you have this pattern in mind:
Code: Select all
+----------+----------+----------+
|  .  12 . |  . 23  . |  . 13  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  . 23  . |  . 13  . |
+----------+----------+----------+

Here e.g. instead of the middle pair you can have
Code: Select all
+----------+----------+----------+
|  .  .  . |  12 .  12|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  12 . |  23 .  . |  .  13 . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  23|  .  13 . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
When you look at T1
Code: Select all
-----------
1..|2..|3..
.2.|3..|1..
...|...|...
-----------
21.|
...|
...|
-----------
you can see, that you have the above 3 digit pattern, where 12 goes around the corner.
ravel
 
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Postby keith » Fri Oct 05, 2007 9:03 pm

Ruud wrote:...

Must be a tough job for the guy who's moderating that forum...


Well, the accusations are probably tough for that guy. Especially since he dares to mention etiquette.

Not to start that same discussion here, but I've been thinking about the objection to using uniqueness techniques on puzzles that are known to have a unique solution.

Is it like assuming that if you drive on the right hand side of the road, you should go counter-clockwise around a traffic circle (roundabout)?

Is it like solving a chess puzzle ("mate in x moves") without proving that the puzzle starting position can be reached in a regular game between opponents of equal skill?

(May I say, I am asking for further analogies, not for arguments on the ethics of uniqueness techniques.)

Keith
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Postby daj95376 » Fri Oct 05, 2007 11:38 pm

I guess everything depends on perspective. I use Uniqueness and don't care if the puzzle has a unique solution or not. If it has a unique solution, then Uniqueness will advance me towards it. If it has multiple solutions, then Uniqueness will advance me towards one of them, or leave me with no solution possible at all.

If I find one solution in a multiple solution puzzle, then I'm done with that puzzle and I won't go back to it. If I get to a position where the puzzle obviously doesn't have a solution, then I'm done with it. Either way, Uniqueness got me through a useless -- I mean multiple solution -- puzzle quicker. Sounds great to me!

Uniqueness isn't the problem, it's the people who expect it to guarantee a unique solution if they use it. If a unique soluton is so critical to you, then use a brute-force program to check for a unique solution before trying to solve the puzzle with logic-based techniques. Then, don't be afraid to use Uniqueness.
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Postby wintder » Sat Oct 06, 2007 12:11 am

daj95376 wrote:If it has multiple solutions, then Uniqueness will advance me towards one of them, or leave me with no solution possible at all.

I quite agree with your post.


I do have a question and that is: can using Uniqueness on a puzzle with multiple solutions result in a position with no solution?

As an aside, if it would be possible to arrive at no solution then using Uniqueness could be a method to show that a puzzle is invalid. (It has no solution or it has multiple solutions.):D
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Postby ravel » Sat Oct 06, 2007 8:17 am

wintder wrote:I do have a question and that is: can using Uniqueness on a puzzle with multiple solutions result in a position with no solution?
Yes
As an aside, if it would be possible to arrive at no solution then using Uniqueness could be a method to show that a puzzle is invalid. (It has no solution or it has multiple solutions.)
It could be sometimes, but this is not a great thing. Normally, when you try to solve a multi solution puzzle manually, you will not have uniqueness options, but will be pretty pretty stuck (and ithis is most annoying).
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