The New Sudoku Players' Forum

[bennys]

Code: Select all

 +-------+-------+-------+
 | 3 1 2 | . . 4 | 9 7 5 |
 | 6 . . | 1 9 7 | 3 2 8 |
 | 8 9 7 | . . . | . 1 . |
 +-------+-------+-------+
 | . . 9 | . 3 1 | 2 . . |
 | . . 3 | 2 . 8 | 1 . 9 |
 | . . 1 | . 4 . | . . 3 |
 +-------+-------+-------+
 | . 3 . | . 1 . | . 9 . |
 | 9 . 6 | 4 . 5 | . 3 1 |
 | 1 . 8 | . . . | 5 . 2 |
 +-------+-------+-------+
 
 +-------------------+-------------------+-------------------+
 | 3     1     2     | 68    68    4     | 9     7     5     |
 | 6    *45    45    | 1     9     7     | 3     2     8     |
 | 8     9     7     | 35   ^25    23    | 46    1     46    |
 +-------------------+-------------------+-------------------+
 | 457   45678 9     | 567   3     1     | 2     4568  467   |
 | 457  *4567  3     | 2    ^567   8     | 1     456   9     |
 | 257   25678 1     | 5679  4     69    | 67    568   3     |
 +-------------------+-------------------+-------------------+
 | 2457  3     45    | 678   1    %26    | 4678  9     467   |
 | 9    *27    6     | 4     278   5     | 78    3     1     |
 | 1    *47    8     | 39   %67    39    | 5     46    2     |
 +-------------------+-------------------+-------------------+

 
 
 A={R9C2,R8C2,R5C2,R2C2}
 B={R9C5,R7C6}
 C={R5C5,R3C5}
                                               
If A B ALS and C with freedom level of 2
x common to A,B,C  (2)
y restricted common to B,C (7)
z restricted common to A,C (6)

then  a cell that can 'see' all the x candidates of  A B and C can't be x.

and we get r8c5<>2 which solve the puzzle.


[ronk]

Code: Select all

 A={R9C2,R8C2,R5C2,R2C2}
 B={R9C5,R7C6}
 C={R5C5,R3C5}
                                               
If A B ALS and C with freedom level of 2
x common to A,B,C  (2)
y restricted common to B,C (7)
z restricted common to A,C (6)

then  a cell that can 'see' all the x candidates of  A B and C can't be x.

and we get r8c5<>2 which solve the puzzle.


Very nice. Here's another viewpoint for the almost locked sets ... the doubly-weakly-linked almost locked sets ...

Code: Select all


     other
       |
       A
     /   \
    z     x . . . x* (elimination)
    .     .     . .
    .     .   .   .
    .     . .     .
    z     x . . . x
     \\ //         \
       C            B -- other
     // \\         /
  other   y . . . y

Set properties:
   If A does not contain z, then A contains x
   If B does not contain y, then B contains x
   If C contains neither y nor z, then C contains x

For your example, the triple implication chains are:

r5c5=5 => r3c5<>5 => r3c5=2 => r8c5<>2 [edit: typo corrected]
r5c5=6 => r5c2<>6 => r8c2=2 => r8c5<>2
r5c5=7 => r9c5<>7 => r7c6=2 => r8c5<>2

P.S. I would normally assign 'z' to the elimination digit, and 'A' to the set with '2 degrees of freedom' ... but followed your labeling for continuity.

[bennys]

You have typo in the first chain