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Sudoku Solution Path

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R4C4 can only be <7>
R4C9 can only be <5>
R5C5 can only be <5>
R6C9 can only be <1>
R4C1 can only be <6>
R6C4 can only be <9>
R6C6 can only be <6>
R5C7 can only be <6>
R5C3 can only be <4>
R6C1 can only be <7>
R4C6 can only be <2>
R3C1 is the only square in row 3 that can be <1>
R7C7 is the only square in row 7 that can be <1>
R9C7 is the only square in row 9 that can be <5>
R3C8 is the only square in row 3 that can be <5>
Intersection of column 7 with block 3. The values <23> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
   R1C9 - removing <2> from <2489> leaving <489>
   R3C9 - removing <2> from <28> leaving <8>
R2C3 is the only square in row 2 that can be <8>
R2C7 is the only square in row 2 that can be <3>
R8C8 is the only square in row 8 that can be <8>
R7C1 is the only square in row 7 that can be <8>
Squares R3C3 and R3C5 in row 3 and R7C3 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 5 can be removed.
   R1C3 - removing <3> from <237> leaving <27>
   R9C3 - removing <3> from <237> leaving <27>
Squares R1C3 and R9C3 in column 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C3 - removing <27> from <2367> leaving <36>
   R7C3 - removing <27> from <2379> leaving <39>
   R8C3 - removing <7> from <679> leaving <69>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.
   R7C9 - removing <4> from <249> leaving <29>
Squares R1C3 and R9C3 in column 3 and R1C6 and R9C6 in column 6 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 1 and 9 can be removed.
   R1C7 - removing <7> from <279> leaving <29>
Squares R9C9 (XY), R9C3 (XZ) and R7C8 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
   R7C2 - removing <7> from <247> leaving <24>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R3C2=<26>
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
   R3C2 - removing <26> from <267> leaving <7>
R3C5 can only be <3>
R3C7 can only be <2>
R2C2 can only be <4>
R8C2 can only be <6>
R1C3 can only be <2>
R3C3 can only be <6>
R7C5 can only be <7>
R1C4 can only be <8>
R1C7 can only be <9>
R7C8 can only be <4>
R9C6 can only be <8>
R7C2 can only be <2>
R2C8 can only be <7>
R9C9 can only be <2>
R8C3 can only be <9>
R8C7 can only be <7>
R7C3 can only be <3>
R9C4 can only be <3>
R1C6 can only be <7>
R9C3 can only be <7>
R7C9 can only be <9>
R1C9 can only be <4>
R1C1 can only be <3>
R9C1 can only be <4>


 

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