## BUG problem

Advanced methods and approaches for solving Sudoku puzzles

### BUG problem

Here is a BUG+2. SS wants to do some coloring to eliminate some 5's. I would like to look at it using BUG rules.

Code: Select all
`  *-----------* |8.9|.5.|...| |26.|...|.8.| |...|..7|6..| |---+---+---| |1..|8..|..2| |...|973|...| |7..|..5|..3| |---+---+---| |..1|7..|...| |.2.|...|.46| |...|.1.|2.8| *-----------* *--------------------------------------------------* | 8    7    9    | 6    5    4    | 3    2    1    | | 2    6    45   | 3    9    1    | 45   8    7    | | 35   1    34   | 2    8    7    | 6    59   459  | |----------------+----------------+----------------| | 1    359  35   | 8    4    6    | 7    59   2    | | 6    45   2    | 9    7    3    | 8    1    45   | | 7    49   8    | 1    2    5    | 49   6    3    | |----------------+----------------+----------------| | 4    8    1    | 7    6    2    | 59   3    59   | | 9    2    7    | 5    3    8    | 1    4    6    | | 35   35   6    | 4    1    9    | 2    7    8    | *--------------------------------------------------*`

Eliminating the 5 from r4c2 forces this into a BUG+1 and then 5 must be placed in r3c9 by a BUG rule.

But eliminating the 5 from r3c9(invalid move) puts the grid in a BUG+1 which would fix a 5 at r4c2(invalid move).

How does this comply with the known BUG rules? In order to know whihc BUG+1 is correct one would have to look at another method. It seems that simply identifying an elimination that leads to a BUG+1 is not enough.

What is the best way to look at this?
doduff

Posts: 32
Joined: 29 May 2006

Code: Select all
` *--------------------------------------------------*  | 8    7    9    | 6    5    4    | 3    2    1    |  | 2    6    45   | 3    9    1    | 45   8    7    |  | 35   1    34   | 2    8    7    | 6    59   49+5 |  |----------------+----------------+----------------|  | 1    39+5 35   | 8    4    6    | 7    59   2    |  | 6    45   2    | 9    7    3    | 8    1    45   |  | 7    49   8    | 1    2    5    | 49   6    3    |  |----------------+----------------+----------------|  | 4    8    1    | 7    6    2    | 59   3    59   |  | 9    2    7    | 5    3    8    | 1    4    6    |  | 35   35   6    | 4    1    9    | 2    7    8    |  *--------------------------------------------------* `

I wouldn't trust a method just because it leads to a BUG+1, I would instead use:

if r7c9=5 (=> r3c9<>5) => r5c9=4 => r5c2=5 (=> r4c2<>5) => r7c9<>5

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

RW wrote:I wouldn't trust a method just because it leads to a BUG+1 ...

In the The BUG (Bivalue Universal Grave) principle thread ...
Jeff wrote:Corollary 4: Any placement of a candidate which forces a grid into a BUG+1 is a valid move. (example)

doduff wrote:Eliminating the 5 from r4c2 forces this into a BUG+1 and then 5 must be placed in r3c9 by a BUG rule.

Note that the corollary requires a placement rather than an exclusion.
Last edited by ronk on Sat Jun 03, 2006 10:31 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

AH.. I see. One must read these things very carefully.

Thanks.
doduff

Posts: 32
Joined: 29 May 2006

RW wrote:if r7c9=5 (=> r3c9<>5) => r5c9=4 => r5c2=5 (=> r4c2<>5) => r7c9<>5

Or: [r7c9]-5-[r7c7]-9-[r6c7]-4-[r5c9]-5-[r7c9], => r7c9<>5.

Carcul
Carcul

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Joined: 04 November 2005