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Aligned Pair Exclusion
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|The Aligned Pair Exclusion can be succinctly stated: Any two cells aligned on a row or column within the same box CANNOT duplicate the contents of any two-candidate cell they both see.
The Y-Wing strategy has some diagrams (see Figure 2) to show how cells can see other cells along the row, column or box and how they intersect or overlap. In Figure 1 [F8/F9] (ringed in green) are the two cells we want to reduce and both cells can see the yellow, green and orange cells.
Lets consider all the possible pairs of numbers that will fit in [F8/F9].
Excluding 1/1 and 6/6 (which are impossible), these are:
1 and 5
1 and 6
2 and 1
2 and 5
2 and 6
6 and 1
6 and 5
9 and 1
9 and 5
9 and 6
APE example 1: Load Example or : From the Start
|The Extended Aligned Pair Exclusion includes tri-values spread over two cells as part of the attack. APE 2 Says that any two cells with only abc excludes combinations ab, ac and bc from the pair under consideration.
This example is very clear since tri-value in [D9/F9] is conveniently 5/6/9 in both cells. (see next example for alternative tri-value formations).
Lets consider all the possible pairs of numbers in [H9/J9] first. These are:
1 and 3
6 and 3
9 and 3
1 and 9
6 and 9
Extended APE example 1: Load Example or : From the Start
In this second example there are two-cell tri-value groups. [A4/B4] containing 6/8/9 gives us the combinations 6/8, 6/9 and 8/9 while [A2/A9] gives us 1/5, 5/9 and 1/9.
All the possible pairs of numbers in the target cells [A5/A6] are:
5 and 4
6 and 4
8 and 4
So that removes 9 from any combinated and we can place 4 in A6 and crack on with the puzzle.
Extended APE example 2: Load Example or : From the Start