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Sudoku Solution Path

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R3C7 is the only square in row 3 that can be <3>
R5C4 is the only square in row 5 that can be <4>
R1C5 is the only square in row 1 that can be <4>
R7C5 is the only square in row 7 that can be <3>
R9C5 is the only square in row 9 that can be <2>
R9C4 is the only square in row 9 that can be <5>
R1C1 is the only square in row 1 that can be <5>
R1C2 is the only square in row 1 that can be <2>
R2C5 is the only square in row 2 that can be <5>
R3C4 is the only square in column 4 that can be <6>
R7C7 is the only square in column 7 that can be <1>
R7C3 is the only square in row 7 that can be <7>
R1C6 is the only square in block 2 that can be <7>
R1C9 is the only square in row 1 that can be <1>
Squares R7C4 and R7C6 in block 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C5 - removing <9> from <169> leaving <16>
   R9C6 - removing <9> from <169> leaving <16>
Intersection of row 2 with block 1. The value <1> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R3C3 - removing <1> from <189> leaving <89>
R5C3 is the only square in column 3 that can be <1>
R5C9 is the only square in row 5 that can be <5>
R4C3 is the only square in row 4 that can be <5>
Intersection of column 7 with block 6. The values <279> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
   R4C9 - removing <79> from <6789> leaving <68>
   R5C8 - removing <79> from <3679> leaving <36>
   R6C9 - removing <79> from <3789> leaving <38>
Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R2C9 - removing <8> from <789> leaving <79>
Squares R5C2<39>, R5C6<69> and R5C8<36> in row 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C1 - removing <39> from <2379> leaving <27>
   R5C7 - removing <9> from <279> leaving <27>
Squares R3C3 and R6C3 in column 3, R3C5, R4C5 and R6C5 in column 5 and R4C7 and R6C7 in column 7 form a Swordfish pattern on possibility <9>. All other instances of this possibility in rows 3, 4 and 6 can be removed.
   R4C1 - removing <9> from <789> leaving <78>
   R6C1 - removing <9> from <23789> leaving <2378>
   R3C6 - removing <9> from <189> leaving <18>
Squares R5C1, R5C7, R6C1 and R6C7 form a Type-3 Unique Rectangle on <27>. Upon close inspection, it is clear that:
(R6C1 or R6C7)<389>, R6C9<38> and R6C3<89> form a locked triplet on <389> in row 6. No other squares in the row can contain these possibilities
   R6C5 - removing <9> from <79> leaving <7>
Squares R4C1 (XY), R4C7 (XZ) and R6C3 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R6C7 - removing <9> from <29> leaving <2>
R5C7 can only be <7>
R5C1 can only be <2>
R4C7 can only be <9>
R4C5 can only be <6>
R4C9 can only be <8>
R8C5 can only be <1>
R5C6 can only be <9>
R4C1 can only be <7>
R6C9 can only be <3>
R5C2 can only be <3>
R7C6 can only be <8>
R6C1 can only be <8>
R5C8 can only be <6>
R7C4 can only be <9>
R3C6 can only be <1>
R3C5 can only be <9>
R9C6 can only be <6>
R3C3 can only be <8>
R1C4 can only be <8>
R6C3 can only be <9>
R1C8 can only be <9>
R8C8 can only be <3>
R2C9 can only be <7>
R2C8 can only be <8>
R9C9 can only be <9>
R8C1 can only be <9>
R9C8 can only be <7>
R9C2 can only be <1>
R8C9 can only be <6>
R8C2 can only be <8>
R2C1 can only be <1>
R9C1 can only be <3>
R2C2 can only be <9>

 

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