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Sudoku Solution Path

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R3C6 can only be <6>
R5C8 can only be <5>
R6C3 can only be <5>
R6C5 can only be <2>
R7C4 can only be <4>
R5C6 can only be <7>
R6C6 can only be <4>
R4C3 can only be <7>
R2C5 can only be <8>
R6C7 can only be <6>
R4C4 can only be <6>
R6C4 can only be <3>
R4C7 can only be <4>
R3C4 can only be <2>
R3C8 can only be <1>
R4C5 can only be <1>
R2C3 can only be <2>
R5C2 can only be <3>
R4C6 can only be <5>
R8C5 can only be <7>
R2C7 can only be <5>
R5C4 can only be <8>
R5C5 can only be <9>
R7C6 can only be <1>
R2C9 can only be <4>
R2C1 can only be <7>
R8C1 is the only square in row 8 that can be <3>
Squares R1C7 and R3C9 in block 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R1C9 - removing <89> from <2689> leaving <26>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.
   R1C1 - removing <9> from <159> leaving <15>
   R8C9 - removing <9> from <69> leaving <6>
R1C9 can only be <2>
R9C8 can only be <7>
R7C8 can only be <2>
R1C8 can only be <6>
R7C2 is the only square in row 7 that can be <7>
R9C3 is the only square in row 9 that can be <6>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R9C1=<14>
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
   R9C1 - removing <14> from <145> leaving <5>
R9C2 can only be <4>
R9C9 can only be <8>
R1C1 can only be <1>
R7C1 can only be <9>
R3C2 can only be <8>
R9C7 can only be <1>
R3C9 can only be <9>
R1C3 can only be <9>
R1C7 can only be <8>
R8C3 can only be <1>
R3C1 can only be <4>
R1C2 can only be <5>
R7C9 can only be <5>
R8C7 can only be <9>

 

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