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Sudoku Solution Path

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R2C1 can only be <9>
R7C4 can only be <3>
R7C6 can only be <5>
R7C7 can only be <6>
R1C1 can only be <5>
R7C3 can only be <8>
R3C3 can only be <2>
R3C4 can only be <9>
R3C7 can only be <1>
R3C6 can only be <8>
R2C5 is the only square in row 2 that can be <3>
R2C9 is the only square in row 2 that can be <4>
R6C2 is the only square in row 6 that can be <5>
R8C8 is the only square in row 8 that can be <5>
R5C1 is the only square in column 1 that can be <7>
R8C5 is the only square in column 5 that can be <7>
R9C5 is the only square in column 5 that can be <4>
R9C1 can only be <1>
R8C4 can only be <2>
R8C6 can only be <1>
R8C1 can only be <4>
Squares R8C2 and R9C2 in column 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R4C2 - removing <39> from <1239> leaving <12>
Squares R4C7 and R6C7 in block 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C8 - removing <2> from <123> leaving <13>
   R5C8 - removing <2> from <1268> leaving <168>
   R5C9 - removing <2> from <28> leaving <8>
   R6C8 - removing <2> from <236> leaving <36>
Intersection of column 9 with block 9. The value <3> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R9C8 - removing <3> from <239> leaving <29>
Squares R8C2, R8C9, R9C2 and R9C9 form a Type-1 Unique Rectangle on <39>.
   R9C9 - removing <39> from <239> leaving <2>
R9C8 can only be <9>
R1C9 can only be <9>
R8C9 can only be <3>
R8C2 can only be <9>
R9C2 can only be <3>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R4C6=<79>
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
   R4C6 - removing <79> from <279> leaving <2>
R4C2 can only be <1>
R4C7 can only be <4>
R2C6 can only be <7>
R6C6 can only be <9>
R5C5 can only be <6>
R4C4 can only be <7>
R6C7 can only be <2>
R5C8 can only be <1>
R1C5 can only be <2>
R6C4 can only be <4>
R5C2 can only be <2>
R4C8 can only be <3>
R6C3 can only be <3>
R1C8 can only be <8>
R1C2 can only be <6>
R2C8 can only be <2>
R2C4 can only be <6>
R4C3 can only be <9>
R6C8 can only be <6>
R2C2 can only be <8>


 

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