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Sudoku Solution Path

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R6C9 can only be <1>
R9C6 can only be <4>
R6C1 can only be <8>
R4C9 can only be <3>
R7C5 can only be <1>
R5C7 can only be <7>
R5C6 can only be <3>
R6C6 can only be <6>
R4C5 can only be <8>
R5C5 can only be <4>
R9C4 can only be <2>
R6C4 can only be <5>
R4C6 can only be <7>
R3C5 can only be <5>
R1C6 can only be <8>
R6C5 can only be <2>
R1C4 can only be <3>
R1C8 is the only square in row 1 that can be <7>
R3C7 is the only square in row 3 that can be <2>
R7C3 is the only square in row 7 that can be <6>
R8C9 is the only square in row 8 that can be <2>
R9C2 is the only square in row 9 that can be <7>
Squares R4C1 and R9C1 in column 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C1 - removing <19> from <1369> leaving <36>
   R8C1 - removing <1> from <134> leaving <34>
Intersection of row 7 with block 9. The value <3> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R8C7 - removing <3> from <348> leaving <48>
   R8C8 - removing <3> from <1358> leaving <158>
Intersection of row 9 with block 9. The value <5> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R8C8 - removing <5> from <158> leaving <18>
Squares R8C7 (XY), R8C1 (XZ) and R2C7 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
   R2C1 - removing <3> from <36> leaving <6>
R1C1 can only be <4>
R1C2 can only be <5>
R8C1 can only be <3>
R1C9 can only be <6>
R8C3 is the only square in row 8 that can be <5>
Squares R2C9, R9C9, R2C8 and R9C8 form a Type-4 Unique Rectangle on <59>.
   R2C8 - removing <9> from <3589> leaving <358>
   R9C8 - removing <9> from <159> leaving <15>
Squares R3C8 (XYZ), R7C8 (XZ) and R2C7 (YZ) form an XYZ-Wing pattern on <3>. All squares that are buddies of all three squares cannot be <3>.
   R2C8 - removing <3> from <358> leaving <58>
Squares R2C8<58>, R8C8<18> and R9C8<15> in column 8 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C8 - removing <8> from <389> leaving <39>
R3C2 is the only square in row 3 that can be <8>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R2C3=<13>
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
   R2C3 - removing <13> from <139> leaving <9>
R2C2 can only be <1>
R2C9 can only be <5>
R3C3 can only be <3>
R5C3 can only be <1>
R2C8 can only be <8>
R9C9 can only be <9>
R3C8 can only be <9>
R7C8 can only be <3>
R5C4 can only be <9>
R4C1 can only be <9>
R4C4 can only be <1>
R7C7 can only be <4>
R9C1 can only be <1>
R8C2 can only be <4>
R2C7 can only be <3>
R8C8 can only be <1>
R7C2 can only be <9>
R8C7 can only be <8>
R9C8 can only be <5>


 

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