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Sudoku Solution Path

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R2C6 can only be <5>
R4C8 can only be <3>
R5C1 can only be <4>
R6C6 can only be <2>
R8C4 can only be <3>
R2C4 can only be <9>
R4C6 can only be <4>
R8C6 can only be <6>
R5C5 can only be <9>
R4C2 can only be <8>
R5C9 can only be <2>
R1C5 can only be <3>
R6C4 can only be <8>
R9C9 can only be <8>
R6C8 can only be <9>
R6C2 can only be <3>
R4C4 can only be <5>
R9C5 can only be <4>
R2C3 is the only square in row 2 that can be <8>
R3C9 is the only square in row 3 that can be <6>
R3C7 is the only square in row 3 that can be <7>
R7C3 is the only square in row 7 that can be <6>
R7C2 is the only square in row 7 that can be <7>
Squares R3C8 and R7C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C8 - removing <4> from <124> leaving <12>
   R8C8 - removing <4> from <124> leaving <12>
Intersection of row 2 with block 3. The value <1> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R1C7 - removing <1> from <129> leaving <29>
Intersection of row 3 with block 1. The values <39> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
   R1C1 - removing <9> from <159> leaving <15>
Intersection of row 7 with block 9. The values <45> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
   R8C7 - removing <4> from <1249> leaving <129>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 7 can be removed.
   R2C7 - removing <2> from <124> leaving <14>
   R8C3 - removing <2> from <124> leaving <14>
   R8C7 - removing <2> from <129> leaving <19>
Squares R1C3 (XY), R8C3 (XZ) and R2C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R8C2 - removing <4> from <249> leaving <29>
   R3C3 - removing <4> from <34> leaving <3>
R8C3 is the only square in row 8 that can be <4>
Intersection of row 8 with block 9. The value <1> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R9C7 - removing <1> from <123> leaving <23>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R7C7=<34>
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
   R7C7 - removing <34> from <349> leaving <9>
R7C1 can only be <3>
R7C9 can only be <5>
R1C7 can only be <2>
R8C7 can only be <1>
R7C8 can only be <4>
R1C9 can only be <9>
R8C8 can only be <2>
R2C7 can only be <4>
R8C2 can only be <9>
R2C8 can only be <1>
R9C7 can only be <3>
R9C1 can only be <1>
R1C3 can only be <1>
R2C2 can only be <2>
R3C8 can only be <5>
R3C1 can only be <9>
R3C2 can only be <4>
R9C3 can only be <2>
R1C1 can only be <5>


 

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