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Sudoku Solution Path

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R2C2 can only be <7>
R2C8 can only be <5>
R1C7 is the only square in row 1 that can be <7>
R6C4 is the only square in row 6 that can be <3>
R7C1 is the only square in row 7 that can be <3>
R8C8 is the only square in row 8 that can be <2>
R1C3 is the only square in column 3 that can be <8>
R5C7 is the only square in column 7 that can be <2>
R5C6 is the only square in row 5 that can be <5>
R4C9 is the only square in row 4 that can be <5>
R9C7 is the only square in row 9 that can be <5>
R3C3 is the only square in column 3 that can be <2>
R1C1 can only be <1>
R3C1 can only be <6>
R1C4 is the only square in row 1 that can be <2>
R3C9 is the only square in column 9 that can be <1>
R4C5 is the only square in column 5 that can be <1>
R4C1 is the only square in row 4 that can be <2>
R6C5 is the only square in row 6 that can be <2>
R6C9 is the only square in column 9 that can be <8>
Squares R6C1 and R6C8 in row 6 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 row.
   R6C2 - removing <4> from <469> leaving <69>
   R6C6 - removing <47> from <4679> leaving <69>
Intersection of row 5 with block 5. The value <4> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
   R4C4 - removing <4> from <489> leaving <89>
   R4C6 - removing <4> from <4789> leaving <789>
Intersection of column 3 with block 7. The value <9> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
   R8C2 - removing <9> from <469> leaving <46>
Intersection of row 8 with block 8. The value <9> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
   R7C5 - removing <9> from <479> leaving <47>
   R9C4 - removing <9> from <1469> leaving <146>
   R9C6 - removing <9> from <14679> leaving <1467>
R3C5 is the only square in column 5 that can be <9>
R3C7 can only be <4>
R1C6 can only be <4>
R7C7 can only be <9>
R1C9 can only be <9>
R9C3 is the only square in row 9 that can be <9>
Squares R6C6 and R8C6 in column 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R4C6 - removing <9> from <789> leaving <78>
   R9C6 - removing <6> from <167> leaving <17>
Squares R6C2 and R8C2 in column 2 and R6C6 and R8C6 in column 6 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 6 and 8 can be removed.
   R8C4 - removing <6> from <469> leaving <49>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R9C4=<16>
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
   R9C4 - removing <16> from <146> leaving <4>
R9C1 can only be <7>
R9C9 can only be <6>
R5C4 can only be <6>
R8C4 can only be <9>
R7C5 can only be <7>
R7C9 can only be <4>
R5C3 can only be <7>
R6C6 can only be <9>
R6C2 can only be <6>
R8C6 can only be <6>
R4C4 can only be <8>
R7C3 can only be <6>
R5C5 can only be <4>
R9C6 can only be <1>
R8C2 can only be <4>
R6C1 can only be <4>
R2C6 can only be <8>
R2C4 can only be <1>
R4C6 can only be <7>
R4C8 can only be <4>
R4C2 can only be <9>
R6C8 can only be <7>

 

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