single digit: Deadly patterns.

Advanced methods and approaches for solving Sudoku puzzles

single digit: Deadly patterns.

Postby StrmCkr » Fri May 23, 2008 7:13 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:13 am, edited 2 times in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby RW » Fri May 23, 2008 8:21 am

I wouldn't really call that a deadly pattern. A deadly pattern is defined as a pattern that can be solved in many different ways (=multiple solutions). Your pattern is just a basic situation of "no candidate 1 in column 5" (=no solutions). The elimination in your example can be described with simple coloring. There are some more interesting "invalid fish patterns", discussed earlier in this thread.

Btw. your puzzle can also be solved with my farvourite (very rare) technique, the Reverse-BUG:
Code: Select all
 *-----------------------*
 | 3*1 - | 9 . 4 | 6 2 5 |
 | 9 6 . | 3 2 . | 4 8 . |
 | 4 2 . | . 6 . | 3 . 9 |
 |-------+-------+-------|
 | 8 3 9 | 5 . 2 | . 6 4 |
 | 2 4 6 | . 9 . | 5 3 . |
 | 5*7*1 | 4 3 6 | 2 9 8 |
 |-------+-------+-------|
 | . . 4 | 2 . 3 | . 5 6 |
 | . 5 3 | 6 4 9 | 8 . 2 |
 | 6 . 2 | . 5 . | . 4 3 |
 *-----------------------*


RW
RW
2010 Supporter
 
Posts: 1000
Joined: 16 March 2006

Postby StrmCkr » Fri May 23, 2008 8:24 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:13 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby StrmCkr » Fri May 23, 2008 8:31 am

deleted
Last edited by StrmCkr on Sat Dec 13, 2014 6:12 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby RW » Fri May 23, 2008 8:39 am

StrmCkr wrote:i don't think this is acutally rare at all, ive seen that pattern alot in many random puzzles.

It is... I've heard many people say before that it shouldn't be rare at all, but this has usually been because of some kind of misunderstanding, like this. It seems to be easy to miss the word that appears bolded and/or underlined several times in the thread: ALL given digits A and B must be included. Your example is a valid Reverse-BUG because there are no other digits 1 or 7 on the grid. If there was, then you can't make any elimination.

RW
RW
2010 Supporter
 
Posts: 1000
Joined: 16 March 2006

Postby StrmCkr » Fri May 23, 2008 8:57 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:12 am, edited 2 times in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby tarek » Fri May 23, 2008 9:01 am

StrmCkr wrote:i was wondering if it was possible to use patterns like this to create strange anit zero solutuions patterns - based on this type of approch instead of muti coloring?
The Nishio algorithm would search for a contradiction or your 0 solutions using a single digit.

tarek
User avatar
tarek
 
Posts: 2622
Joined: 05 January 2006

Postby StrmCkr » Fri May 23, 2008 9:08 am

removed.
Last edited by StrmCkr on Sat Dec 13, 2014 6:12 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby RW » Fri May 23, 2008 9:13 am

StrmCkr wrote:but i see what i did missed represent though, placing 7 in the "-' leaves solution leaves a muti solution grid. not a rectangle pattern.

Perhaps a bit of nitpicking, but you don't make uniqueness eliminations because the eliminated numbers would leave a multi solution grid, you make them because they would leave a grid that cannot have a unique solution (either 0 or >1 solutions). In all valid puzzles, this means that the eliminated digit would lead to a grid with no solutions.

The main reason why I think this technique is rare is that I hardly ever see any puzzles where it can be applied. I think this is the first time I see a 4-cell Reverse-BUG in a puzzle that I haven't constructed myself especially for this purpose. The real reason why small Reverse-BUG patterns are rare is that they require a special kind of 2-rookery in the solution, from which only a small number of digits placed in a certain way can be featured as givens. This rarely happens by accident...

RW
RW
2010 Supporter
 
Posts: 1000
Joined: 16 March 2006

Postby tarek » Fri May 23, 2008 9:28 am

StrmCkr wrote:doest it do it using a brute force/ trial error method?
closer to T&E IMO. I hate colouring techniques myself & took the fishy way for single digit eliminations

tarek
User avatar
tarek
 
Posts: 2622
Joined: 05 January 2006

Postby StrmCkr » Fri May 23, 2008 9:30 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:11 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 647
Joined: 05 September 2006

Postby RW » Fri May 23, 2008 11:27 am

StrmCkr wrote:
Perhaps a bit of nitpicking, but you don't make uniqueness eliminations because the eliminated numbers would leave a multi solution grid, you make them because they would leave a grid that cannot have a unique solution (either 0 or >1 solutions). In all valid puzzles, this means that the eliminated digit would lead to a grid with no solutions.


i read that as saying the same thing twice.

muti solution grids are invalid for any puzzle that must have only one solution.

A unique puzzle can never end up in a multi solution grid - A multi solution grid is not invalid, it is impossible. Multi solution subpatterns of the grid are invalid, because they would cause the grid to have no solutions. There is a fine difference there.

heres a randomly generated puzzle.

4 at the @ are eliminated using revese bug if i got it right.

No. The basic idea with the Reverse-BUG is that if the already solved cells of two digits form an unavoidable set, then the remaining unsolved cells make up a deadly pattern. In your example, no matter how you fill in the remaining digits 4 and 9, you have solved all digits 4 and 9 in the puzzle. So where is the deadly pattern?

RW
RW
2010 Supporter
 
Posts: 1000
Joined: 16 March 2006


Return to Advanced solving techniques