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Sudoku Solution Path

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R8C8 can only be <8>
R4C3 is the only square in row 4 that can be <9>
R5C4 is the only square in row 5 that can be <3>
R8C7 is the only square in row 8 that can be <3>
R9C6 is the only square in column 6 that can be <4>
R9C7 is the only square in column 7 that can be <9>
R9C4 can only be <5>
R2C5 is the only square in column 5 that can be <5>
R2C3 is the only square in row 2 that can be <8>
Intersection of row 9 with block 7. The value <6> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
   R7C1 - removing <6> from <1267> leaving <127>
   R7C2 - removing <6> from <2679> leaving <279>
Intersection of column 4 with block 2. The value <2> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R3C5 - removing <2> from <1279> leaving <179>
Intersection of column 7 with block 3. The value <2> 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 this value.
   R1C9 - removing <2> from <2357> leaving <357>
   R3C9 - removing <2> from <2347> leaving <347>
Intersection of block 5 with column 5. The values <28> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.
   R7C5 - removing <8> from <1689> leaving <169>
Squares R3C1 and R6C1 in column 1 and R3C9 and R6C9 in column 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 3 and 6 can be removed.
   R3C2 - removing <4> from <2467> leaving <267>
   R6C3 - removing <4> from <2467> leaving <267>
   R3C8 - removing <4> from <467> leaving <67>
Squares R1C3, R6C3 and R9C3 in column 3 form a simple locked triplet. These 3 squares all contain the 3 possibilities <267>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R5C3 - removing <267> from <12467> leaving <14>
Squares R3C2<267>, R3C4<29>, R3C5<179>, R3C6<17> and R3C8<67> in row 3 form a comprehensive locked set. These 5 squares can only contain the 5 possibilities <12679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C1 - removing <267> from <23467> leaving <34>
   R3C9 - removing <7> from <347> leaving <34>
Squares R3C2 and R5C2 in column 2 and R3C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 3 and 5 can be removed.
   R5C5 - removing <6> from <267> leaving <27>
   R5C6 - removing <6> from <67> leaving <7>
   R5C7 - removing <6> from <1567> leaving <157>
R5C5 can only be <2>
R1C6 can only be <8>
R3C6 can only be <1>
R1C4 can only be <2>
R7C6 can only be <6>
R3C4 can only be <9>
R3C5 can only be <7>
R7C4 can only be <8>
R3C8 can only be <6>
R3C2 can only be <2>
R2C7 is the only square in row 2 that can be <2>
R5C2 is the only square in row 5 that can be <6>
Squares R2C2 and R7C2 in column 2 and R2C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 2 and 7 can be removed.
   R7C1 - removing <7> from <127> leaving <12>
   R7C9 - removing <7> from <257> leaving <25>
Squares R2C8 (XY), R5C8 (XZ) and R1C7 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
   R5C7 - removing <5> from <15> leaving <1>
R5C3 can only be <4>
R5C8 can only be <5>
R8C3 can only be <1>
R7C8 can only be <7>
R7C2 can only be <9>
R2C8 can only be <4>
R9C9 can only be <2>
R8C5 can only be <9>
R7C1 can only be <2>
R8C2 can only be <4>
R7C5 can only be <1>
R7C9 can only be <5>
R2C2 can only be <7>
R3C9 can only be <3>
R3C1 can only be <4>
R6C1 can only be <7>
R1C9 can only be <7>
R1C3 can only be <6>
R1C7 can only be <5>
R4C9 can only be <8>
R4C5 can only be <6>
R6C9 can only be <4>
R6C3 can only be <2>
R6C7 can only be <6>
R4C1 can only be <1>
R9C1 can only be <6>
R6C5 can only be <8>
R4C7 can only be <7>
R9C3 can only be <7>
R1C1 can only be <3>


 

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