In order forcing chains logic to detect this pattern there would have to be a new link type, perhaps called an
extended disjoint subset link that could deduce r6c2=9 => r5c3=4. It might be written r6c2 -><9|4>->r5c3, or something similar in order to suggest the lack of symmetry. The general pattern is that when a cell in a sector that contains an Almost Disjoint Subset / Locked Set takes a value associated with that set, the set is locked, so any value in that set that is a candidate for just one position must take its position.
With this link type, the critical chain would be:
r6c2-><9|4>->r5c3-4-r1c3+<4|5>+r1c8~5~r2c7+<5|9>+r6c7-9-r6c2, which is self-contradictory if r6c2 contains 9.
Without this link type, it's possible to make good progress:
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Consider the chain r2c3+<7|3>+r2c7~3~r5c7-4-r5c3+<4|6>+r8c3.
When the cell r2c3 contains the value 6, so does the cell r8c3 - a contradiction.
Therefore, the cell r2c3 cannot contain the value 6.
- The move r2c3:=6 has been eliminated.
The cell r8c3 is the only candidate for the value 6 in Column 3.
Unfortunately, this chain isn't a killer. After some straightforward progress:
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2. The cell r8c1 is the only candidate for the value 1 in Row 8.
3. The cell r2c2 is the only candidate for the value 6 in Row 2.
4. The cell r9c7 is the only candidate for the value 6 in Row 9.
5. The value 5 in Box 7 must lie in Row 9.
- The move r8c2:=5 has been eliminated.
The cell r9c2 is the only candidate for the value 5 in Column 2.
6. Consider the chain r8c2-9-r6c2~9~r6c7-9-r8c7.
The cell r8c7 must contain the value 9 if the cell r8c2 doesn't.
Therefore, these two cells are the only candidates for the value 9 in Row 8.
- The moves r8c5:=9, r8c6:=9 and r8c9:=9 have been eliminated.
Consider the chain r6c2-9-r8c2-9-r8c7-9-r6c7.
The cell r6c7 must contain the value 9 if the cell r6c2 doesn't.
Therefore, these two cells are the only candidates for the value 9 in Row 6.
- The move r6c1:=9 has been eliminated.
the following candidate grid remains:
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4|5|9 1 4|7 | 7|8 3 8|9 | 2 5|8 6
5|9 6 7|9 | 2|7|8 2|8|9 4 | 3|5 1|3|5|8 1|3
8 3 2 | 5 6 1 | 7 9 4
----------------------+----------------------+-------------------------
3|9 7 1|3|9 | 6 4 5 | 8 1|2|3 1|2|3|9
6 2|8 1|3|4 | 9 2|8 7 | 3|4 1|3 5
2|4 2|8|9 5 | 2|3|8 1 2|3|8 | 4|9 6 7
----------------------+----------------------+-------------------------
7 4 3|9 | 2|3 2|5|9 6 | 1 2|3|5 8
1 2|9 6 | 4 2|5|8 2|3|8 | 3|5|9 7 2|3
2|3|9 5 8 | 1 7 2|3|9 | 6 4 2|3|9
whereupon the puzzle falls to the following observation:
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Consider the cell r6c1.
When it contains the value 4, the values 5 and 9 in Column 1 must occupy the cells r1c1 and r2c1 in some order.
When it contains the value 2, the values 8 and 9 in Box 4 must occupy the cells r5c2 and r6c2 in some order.
Whichever value it contains, the cells r4c1 and r5c1 cannot contain the value 9.
- The move r4c1:=9 has been eliminated.
The value 3 is the only candidate for the cell r4c1.