Is this a BUG-Lite ?

Advanced methods and approaches for solving Sudoku puzzles

Is this a BUG-Lite ?

Postby ronk » Mon Dec 20, 2010 11:22 pm

I've always assumed a BUG-lite had exactly two solutions, and rarely bothered to see if that was actually the case. Here is one, based on a post by peterj here, that has no solution.

Code: Select all
 .  .  .  | .  .  .  | ab ab . 
 ab ab .  | .  .  .  | .  .  . 
 .  .  .  | .  .  .  | .  .  . 
----------+----------+----------
 .  ac .  | .  .  .  | ac .  . 
 .  .  .  | .  .  ac | .  ac . 
 ac .  .  | .  .  ac | .  .  . 
----------+----------+----------
 .  bc .  | .  .  .  | .  bc . 
 .  .  .  | .  .  .  | .  .  . 
 bc .  .  | .  .  .  | bc .  . 

Does anyone think that referring to this pattern as a BUG-Lite is improper?
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Re: Is this a BUG-Lite ?

Postby lksudoku » Tue Dec 21, 2010 7:42 am

a BUG pattern can have an even number of solutions, that is 0,2,4 and so on

Therefore a BUG-lite can also have an even number of solutions
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Re: Is this a BUG-Lite ?

Postby RW » Tue Dec 21, 2010 8:42 am

lksudoku wrote:a BUG pattern can have an even number of solutions, that is 0,2,4 and so on

Therefore a BUG-lite can also have an even number of solutions

In a valid puzzle a BUG (as in BUG+n, all unsolved cells included) always has 0 solutions. As BUG-lite is a lighter version of BUG, a BUG-lite with 0 solutions should of course be accepted.

But in this case the 0 solutions is not caused by the BUG-lite, but by the impossible pattern on candidate c (see below). So essentially, any elimination made using that BUG-lite pattern could have been made as a non-uniqueness elimination using a smaller pattern.

Code: Select all
 .  c  .  | .  .  .  | c  .  .
 .  .  .  | .  .  c  | .  c  .
 c  .  .  | .  .  c  | .  .  .
----------+----------+--------
 .  c  .  | .  .  .  | .  c  .
 .  .  .  | .  .  .  | .  .  .
 c  .  .  | .  .  .  | c  .  .


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