Flipping a Candidate Pair

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Flipping a Candidate Pair

Postby daj95376 » Sun Oct 29, 2006 11:46 pm

While searching for a Deadly Pattern on <89> in a puzzle presented in another thread, I noticed an interesting flipping relationship.

Code: Select all
 *-----------*
 |...|1..|..2|
 |.1.|.5.|...|
 |..7|...|6..|
 |---+---+---|
 |5..|..2|...|
 |.4.|.6.|.7.|
 |...|5..|..1|
 |---+---+---|
 |..2|...|3..|
 |...|.9.|.8.|
 |3..|..1|...|
 *-----------* # Nick70 puzzle presented recently by Ocean

# after basics
 *-----------------------------------------------------------*
 | 4689  689   489   | 1     3     7     | 489   5     2     |
 | 2     1     3     | 489   5     6     | 7     49    489   |
 | 489   5     7     | 489   2     48    | 6     1     3     |
 |-------------------+-------------------+-------------------|
 | 5     3     89    | 7     1     2     | 489   469   4689  |
 | 89    4     1     | 3     6     89    | 2     7     5     |
 | 7     2     6     | 5     48    489   | 89    3     1     |
 |-------------------+-------------------+-------------------|
 | 1     6789  2     | 468   478   5     | 3     469   4679  |
 | 46    67    5     | 2     9     3     | 1     8     467   |
 | 3     6789  489   | 468   478   1     | 5     2     4679  |
 *-----------------------------------------------------------*

Consider the following forcing chains on [r6c7] and note the flipping action on <89> by the time each chain gets to [r1c7].

Code: Select all
[r6c7]-8-[r6c56]=8=[r5c6]=9=[r5c1]-9-[r13c1]=9=[r1c23]-9-[r1c7] => [r1c7]<>8|9
[r6c7]-9-[r6c 6]=9=[r5c6]=8=[r5c1]-8-[r13c1]=8=[r1c23]-8-[r1c7] => [r1c7]<>8|9

Thus, [r1c7]=4 ... and a cascade of Singles solves the puzzle.
daj95376
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