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Sudoku Solution Path

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R5C5 can only be <8>
R4C7 is the only square in row 4 that can be <4>
R5C2 is the only square in row 5 that can be <6>
R2C3 is the only square in row 2 that can be <6>
R6C6 is the only square in row 6 that can be <1>
R6C3 is the only square in row 6 that can be <5>
R7C3 is the only square in row 7 that can be <1>
R7C2 is the only square in row 7 that can be <3>
R7C6 is the only square in row 7 that can be <4>
R1C5 is the only square in row 1 that can be <4>
R8C3 is the only square in row 8 that can be <4>
R9C5 is the only square in row 9 that can be <1>
R7C4 is the only square in column 4 that can be <8>
R3C6 is the only square in column 6 that can be <7>
R5C8 is the only square in column 8 that can be <3>
Squares R7C7 and R7C8 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C7 - removing <9> from <2589> leaving <258>
   R8C8 - removing <9> from <289> leaving <28>
   R9C9 - removing <9> from <259> leaving <25>
Intersection of column 9 with block 6. The values <78> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
   R6C7 - removing <78> from <2789> leaving <29>
Squares R6C4 and R6C7 in row 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R6C1 - removing <2> from <278> leaving <78>
   R6C9 - removing <29> from <2789> leaving <78>
Squares R5C1 and R5C9 in row 5 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 9 can be removed.
   R1C1 - removing <2> from <239> leaving <39>
   R1C9 - removing <2> from <259> leaving <59>
   R4C1 - removing <2> from <238> leaving <38>
   R4C9 - removing <2> from <289> leaving <89>
Intersection of row 1 with block 2. The value <2> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R3C4 - removing <2> from <2359> leaving <359>
Squares R1C4 and R1C9 in row 1 and R9C4 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 4 and 9 can be removed.
   R3C4 - removing <5> from <359> leaving <39>
Squares R1C1 and R9C1 in column 1, R1C6, R4C6 and R9C6 in column 6 and R1C9 and R4C9 in column 9 form a Swordfish pattern on possibility <9>. All other instances of this possibility in rows 1, 4 and 9 can be removed.
   R1C4 - removing <9> from <2359> leaving <235>
   R4C4 - removing <9> from <269> leaving <26>
   R9C4 - removing <9> from <569> leaving <56>
Squares R7C7, R7C8, R2C7 and R2C8 form a Type-4 Unique Rectangle on <79>.
   R2C7 - removing <9> from <2579> leaving <257>
   R2C8 - removing <9> from <279> leaving <27>
Squares R2C2 and R2C5 in row 2 and R8C2 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 5 can be removed.
   R3C2 - removing <9> from <259> leaving <25>
Squares R4C1 (XY), R1C1 (XZ) and R4C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R1C9 - removing <9> from <59> leaving <5>
R9C9 can only be <2>
R9C1 can only be <9>
R5C9 can only be <7>
R8C8 can only be <8>
R5C1 can only be <2>
R6C9 can only be <8>
R6C1 can only be <7>
R4C9 can only be <9>
R8C7 can only be <5>
R9C6 can only be <6>
R1C1 can only be <3>
R8C2 can only be <2>
R9C4 can only be <5>
R1C4 can only be <2>
R4C1 can only be <8>
R3C3 can only be <2>
R1C6 can only be <9>
R4C4 can only be <6>
R6C4 can only be <9>
R4C6 can only be <2>
R2C5 can only be <5>
R3C4 can only be <3>
R8C5 can only be <9>
R3C2 can only be <5>
R3C8 can only be <9>
R4C3 can only be <3>
R2C2 can only be <9>
R3C7 can only be <8>
R7C8 can only be <7>
R6C7 can only be <2>
R2C7 can only be <7>
R7C7 can only be <9>
R2C8 can only be <2>


 

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