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Sudoku Solution Path

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R2C4 is the only square in row 2 that can be <9>
R2C5 is the only square in row 2 that can be <5>
R1C8 is the only square in row 1 that can be <5>
R3C9 is the only square in row 3 that can be <1>
R5C2 is the only square in row 5 that can be <5>
R8C5 is the only square in row 8 that can be <3>
R8C6 is the only square in row 8 that can be <7>
R9C2 is the only square in row 9 that can be <7>
R9C1 is the only square in row 9 that can be <8>
R8C8 is the only square in block 9 that can be <9>
R5C8 can only be <7>
R3C8 can only be <3>
R2C2 is the only square in row 2 that can be <3>
R1C2 can only be <1>
R1C1 can only be <4>
R1C3 can only be <8>
R1C6 can only be <6>
R2C3 can only be <2>
R1C9 can only be <7>
R1C4 can only be <3>
R6C1 is the only square in row 6 that can be <3>
R4C7 is the only square in row 4 that can be <3>
R8C1 is the only square in row 8 that can be <2>
R7C2 can only be <9>
R6C2 can only be <2>
R7C6 is the only square in row 7 that can be <2>
Squares R3C4 and R6C4 in column 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R4C4 - removing <4> from <145> leaving <15>
   R7C4 - removing <4> from <146> leaving <16>
   R9C4 - removing <4> from <1456> leaving <156>
R7C5 is the only square in row 7 that can be <4>
R4C5 can only be <1>
R9C6 can only be <5>
R4C4 can only be <5>
Intersection of row 5 with block 6. The value <8> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
   R6C9 - removing <8> from <4689> leaving <469>
Squares R2C7 and R2C9 in row 2, R6C3 and R6C9 in row 6 and R8C3 and R8C7 in row 8 form a Swordfish pattern on possibility <6>. All other instances of this possibility in columns 3, 7 and 9 can be removed.
   R4C9 - removing <6> from <2469> leaving <249>
   R9C7 - removing <6> from <146> leaving <14>
   R9C9 - removing <6> from <246> leaving <24>
Squares R4C1 (XY), R6C3 (XZ) and R4C6 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R6C6 - removing <4> from <489> leaving <89>
   R6C4 - removing <4> from <47> leaving <7>
R6C5 can only be <8>
R3C4 can only be <4>
R6C6 can only be <9>
R3C5 can only be <7>
R4C6 can only be <4>
R3C6 can only be <8>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R5C9=<89>
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
   R5C9 - removing <89> from <489> leaving <4>
R5C3 can only be <1>
R5C7 can only be <8>
R6C9 can only be <6>
R9C9 can only be <2>
R6C3 can only be <4>
R2C9 can only be <8>
R4C8 can only be <2>
R9C8 can only be <6>
R4C9 can only be <9>
R2C7 can only be <6>
R4C1 can only be <6>
R5C1 can only be <9>
R8C3 can only be <6>
R8C7 can only be <1>
R7C1 can only be <1>
R9C7 can only be <4>
R9C4 can only be <1>
R7C4 can only be <6>


 

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