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Sudoku Solution Path

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R1C1 can only be <3>
R4C1 can only be <8>
R7C2 can only be <3>
R8C7 can only be <3>
R9C4 can only be <1>
R9C6 can only be <3>
R6C1 can only be <9>
R9C1 can only be <6>
R2C3 can only be <5>
R3C2 can only be <7>
R2C2 can only be <6>
R7C5 can only be <9>
R8C3 can only be <2>
R7C8 can only be <1>
R5C3 can only be <3>
R8C6 can only be <7>
R8C8 can only be <9>
R2C7 can only be <1>
R5C7 can only be <6>
R9C9 can only be <2>
R8C2 can only be <4>
R8C4 can only be <8>
R1C6 can only be <5>
R8C5 can only be <6>
R5C5 is the only square in row 5 that can be <8>
R6C2 is the only square in row 6 that can be <1>
R6C9 is the only square in column 9 that can be <3>
Intersection of column 4 with block 2. The value <7> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R2C5 - removing <7> from <237> leaving <23>
Squares R4C2, R5C2, R4C8 and R5C8 form a Type-3 Unique Rectangle on <25>. Upon close inspection, it is clear that:
(R4C8 or R5C8)<47> and R4C9<47> form a locked pair on <47> in block 6. No other squares in the block can contain these possibilities
   R6C8 - removing <7> from <27> leaving <2>
R6C5 can only be <7>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R4C8=<57>
These are called the BUG possibilities. In a BUG pattern, in each row, column and block, each unsolved possibility appears exactly twice. Such a pattern either has 0 or 2 solutions, so it cannot be part of a valid Sudoku
When a puzzle contains a BUG, and only one square in the puzzle has more than 2 possibilities, the only way to kill the BUG is to remove both of the BUG possibilities from the square, thus solving it
   R4C8 - removing <57> from <457> leaving <4>
R4C5 can only be <2>
R4C9 can only be <7>
R3C8 can only be <3>
R5C8 can only be <5>
R1C9 can only be <4>
R5C2 can only be <2>
R1C4 can only be <7>
R3C5 can only be <4>
R2C8 can only be <7>
R4C2 can only be <5>
R2C5 can only be <3>
R5C6 can only be <9>
R5C4 can only be <4>
R2C6 can only be <2>
R2C4 can only be <9>


 

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