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Sudoku Solution Path

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R1C1 can only be <9>
R5C5 can only be <4>
R3C1 can only be <6>
R9C1 can only be <3>
R5C1 can only be <1>
R7C1 can only be <7>
R2C4 is the only square in row 2 that can be <1>
R2C5 is the only square in row 2 that can be <7>
R1C7 is the only square in row 1 that can be <7>
R3C5 is the only square in row 3 that can be <5>
R3C3 is the only square in row 3 that can be <8>
R4C7 is the only square in row 4 that can be <1>
R3C9 is the only square in row 3 that can be <1>
R4C8 is the only square in row 4 that can be <4>
R2C8 can only be <9>
R5C3 is the only square in row 5 that can be <5>
R6C3 is the only square in row 6 that can be <7>
R6C8 is the only square in row 6 that can be <8>
R8C4 is the only square in row 8 that can be <7>
R8C5 is the only square in row 8 that can be <8>
R7C9 is the only square in row 7 that can be <8>
R9C3 is the only square in row 9 that can be <9>
Squares R4C2 and R4C3 in block 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R5C2 - removing <26> from <2369> leaving <39>
Intersection of row 9 with block 9. The value <4> 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.
   R7C7 - removing <4> from <2346> leaving <236>
Squares R2C2 and R2C6 in row 2 and R8C2 and R8C6 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 6 can be removed.
   R3C6 - removing <4> from <349> leaving <39>
   R7C6 - removing <4> from <2349> leaving <239>
Squares R6C2, R6C7, R5C2 and R5C7 form a Type-1 Unique Rectangle on <39>.
   R5C7 - removing <39> from <2369> leaving <26>
R5C2 is the only square in row 5 that can be <9>
R6C2 can only be <3>
R6C7 can only be <9>
Squares R1C9 (XY), R1C5 (XZ) and R9C9 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R9C5 - removing <2> from <26> leaving <6>
Squares R9C7 and R9C9 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C7 - removing <2> from <236> leaving <36>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R7C6=<29>
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
   R7C6 - removing <29> from <239> leaving <3>
R7C5 can only be <2>
R7C7 can only be <6>
R3C6 can only be <9>
R8C6 can only be <4>
R7C3 can only be <4>
R5C7 can only be <2>
R8C8 can only be <3>
R8C2 can only be <6>
R2C6 can only be <2>
R7C4 can only be <9>
R5C8 can only be <6>
R2C2 can only be <4>
R1C5 can only be <3>
R3C4 can only be <4>
R5C9 can only be <3>
R9C7 can only be <4>
R1C9 can only be <4>
R1C3 can only be <2>
R4C2 can only be <2>
R9C9 can only be <2>
R3C7 can only be <3>
R4C3 can only be <6>


 

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