The New Sudoku Players' Forum

[doduff]

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?

[RW]

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

[ronk]

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

In the The BUG (Bivalue Universal Grave) principle thread ...

Corollary 4: Any placement of a candidate which forces a grid into a BUG+1 is a valid move. (example)

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.

[doduff]

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

Thanks.

[Carcul]

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