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Sudoku Solution Path

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Copyright © Kevin Stone

R5C1 can only be <3>
R2C7 is the only square in row 2 that can be <8>
R3C3 is the only square in row 3 that can be <2>
R3C2 is the only square in row 3 that can be <1>
R5C2 can only be <9>
R5C8 can only be <7>
R4C3 can only be <7>
R5C6 can only be <5>
R5C9 can only be <8>
R6C3 can only be <1>
R5C5 can only be <6>
R5C4 can only be <1>
R3C4 is the only square in row 3 that can be <6>
R4C5 is the only square in row 4 that can be <2>
R4C6 is the only square in row 4 that can be <4>
R6C4 is the only square in row 6 that can be <8>
R7C8 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <8>
R9C7 is the only square in row 9 that can be <1>
R8C3 is the only square in column 3 that can be <9>
R2C3 is the only square in column 3 that can be <6>
Squares R4C7 and R6C7 in column 7 form a simple locked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R1C7 - removing <3> from <345> leaving <45>
   R3C7 - removing <39> from <34579> leaving <457>
   R7C7 - removing <3> from <3567> leaving <567>
   R8C7 - removing <3> from <3567> leaving <567>
Squares R7C4<39>, R7C6<379> and R7C9<37> in row 7 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R7C2 - removing <3> from <346> leaving <46>
   R7C7 - removing <7> from <567> leaving <56>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 5 can be removed.
   R2C5 - removing <3> from <349> leaving <49>
   R6C5 - removing <3> from <379> leaving <79>
   R8C5 - removing <3> from <357> leaving <57>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
   R3C8 - removing <3> from <359> leaving <59>
Squares R8C8 (XY), R8C2 (XZ) and R7C7 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
   R7C2 - removing <6> from <46> leaving <4>
   R8C7 - removing <6> from <567> leaving <57>
R7C1 can only be <5>
R2C2 can only be <3>
R2C8 can only be <9>
R8C2 can only be <6>
R1C3 can only be <5>
R2C5 can only be <4>
R3C8 can only be <5>
R3C1 can only be <4>
R8C8 can only be <3>
R1C7 can only be <4>
R7C7 can only be <6>
R9C3 can only be <3>
R7C9 can only be <7>
R9C5 can only be <5>
R8C5 can only be <7>
R1C5 can only be <3>
R3C7 can only be <7>
R3C9 can only be <3>
R8C7 can only be <5>
R3C6 can only be <9>
R6C5 can only be <9>
R7C6 can only be <3>
R6C7 can only be <3>
R4C4 can only be <3>
R6C6 can only be <7>
R4C7 can only be <9>
R7C4 can only be <9>

[Puzzle Code = Sudoku-20191023-SuperHard-252730]

 

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