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Sudoku Solution Path

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R1C5 can only be <4>
R4C4 can only be <2>
R4C6 can only be <7>
R5C2 can only be <8>
R5C9 can only be <2>
R6C4 can only be <5>
R6C6 can only be <6>
R2C5 can only be <5>
R6C5 can only be <8>
R4C5 can only be <1>
R5C4 can only be <9>
R5C1 can only be <6>
R5C5 can only be <3>
R5C8 can only be <7>
R5C6 can only be <4>
R3C9 is the only square in row 3 that can be <5>
R7C2 is the only square in row 7 that can be <5>
Squares R3C2 and R3C8 in row 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C1 - removing <12> from <128> leaving <8>
   R3C7 - removing <12> from <1247> leaving <47>
R8C1 can only be <2>
R8C5 can only be <9>
R8C9 can only be <4>
R9C5 can only be <2>
Squares R1C7<27>, R2C7<14>, R3C7<47> and R3C8<12> in block 3 form a comprehensive locked quad. These 4 squares can only contain the 4 possibilities <1247>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R1C8 - removing <2> from <239> leaving <39>
Squares R1C3 and R1C8 in row 1 and R9C3 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 8 can be removed.
   R2C3 - removing <3> from <349> leaving <49>
   R7C3 - removing <3> from <369> leaving <69>
   R7C8 - removing <3> from <1239> leaving <129>
Squares R7C1 (XY), R9C2 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R7C3 - removing <9> from <69> leaving <6>
   R9C8 - removing <9> from <139> leaving <13>
R8C3 can only be <8>
R8C7 can only be <6>
R9C7 is the only square in row 9 that can be <8>
Squares R3C2 and R3C8 in row 3 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.
   R7C8 - removing <1> from <129> leaving <29>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C3=<37>
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
   R1C3 - removing <37> from <379> leaving <9>
R1C2 can only be <2>
R1C8 can only be <3>
R2C3 can only be <4>
R9C3 can only be <3>
R9C8 can only be <1>
R2C9 can only be <9>
R2C7 can only be <1>
R3C3 can only be <7>
R2C1 can only be <3>
R7C7 can only be <2>
R3C8 can only be <2>
R7C9 can only be <3>
R3C7 can only be <4>
R3C2 can only be <1>
R7C8 can only be <9>
R1C7 can only be <7>
R7C1 can only be <1>
R9C2 can only be <9>


 

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