## Flipping a Candidate Pair

Everything about Sudoku that doesn't fit in one of the other sections

### Flipping a Candidate Pair

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

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` *-----------* |...|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].

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`[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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Joined: 15 May 2006