In my technique will be used 3 types of cells
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B B B | . . . | . . .
I I I | L L L | L L L
B B B | . . . | . . .
B is part of the Block, L is part of the Line (row or column) and I is part of the block-line interaction.
Lets get two naked pairs, which have one shared candidate {1,2}, {1,2} and {1,3}{1,3}.
If one of the subsets is in the block and the other is in the line we can bind the subsets (distroing them) in a structure named XYZ-Wing
B{1,2}, I{1,2,3}, L{1,3}. In this case all other I cells can not contain the shared candidate, which in this example is
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B {1,2} B | . . .
{1,2,3} I I | L {1,3} L
So, this was for two pairs, more complex situation we will have with pair and triplet. {1,2}, {1,2} and {1,3} {1,4} {3,4}
Binding them we have double subset:
B{1,2} I{1,2,3} L{1,4} L{3,4} and again all other I cells can not contain 1
The situation is going more interesting if we have two triplets. There are two possible variants for them
1) having one shared cell {1,2} {2,3} {3,1} and {1,4} {1,4,5} {1,4,5}
2) having two shared cells {1,2} {1,2,3} {2,3} and {1,2,4} {1,2,4} {1,2}
The second case will look like this:
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{1,2} {2,3} B | . . .
{1,2,3,4} I I | {1,2,4} L {1,2}
If we want to make the things really complicated and interesting we should use at least on quad.
If the quad is bind with pair there can be only one shared candidate, if it is bind with triplet the shared candidates can be 1 or 2.In case it is binded with another quad it is possible to have up to 3 shared candidates.
You don't need example to understand that, so I'm goging to give you example for a different configuration possible only with quads:
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{3,4} {1,4} B | . . .
{1,2} {2,3} I | {3,5} L {1,5}
Here we have 3 shared candidates and 2 used I cells. In this case we can remove candidates only from one cell.
* here is not mandatory to have only 2 candidates for a cell - it's just easier to see the formation, that's why I use such example
Another interesting thing, which completely separate this technique from XYZ-Wing is that it is not mandatory all shared candidates to be candidates for the shared cell.
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{3,4} {1,4} {2,3} | . . .
{1,2} I I | {3,5} {2,3} {1,5}
In this case 3 is also shared cell and all I cells can not be 3.
And just one example how complex this can look:
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. . .| B {1,3,4} {1,2,3} | . . .
{1,3,5} L L|{1,2,5} I I | L {2,3} {1,2,5}
. . .| B {1,2,3,4} B | . . .
Looking ahead the next techniques will be Hidden double subset and Chain subsets
So, it this something new ot not?
If it is new, I'll implement it in my solver and will try to find examples for puzzles which require all kind of this technique.