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Sudoku Solution Path

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Copyright © Kevin Stone

R3C4 can only be <9>
R4C3 can only be <7>
R5C1 can only be <5>
R5C4 can only be <4>
R5C9 can only be <6>
R6C3 can only be <2>
R7C4 can only be <2>
R7C6 can only be <8>
R4C5 can only be <9>
R4C7 can only be <3>
R6C5 can only be <6>
R5C5 can only be <7>
R5C6 can only be <1>
R6C7 can only be <9>
R1C5 can only be <8>
R7C1 can only be <9>
R3C6 can only be <6>
R9C5 can only be <5>
R3C2 is the only square in row 3 that can be <7>
R7C7 is the only square in row 7 that can be <7>
R8C8 is the only square in row 8 that can be <2>
R3C8 is the only square in column 8 that can be <3>
Squares R3C3 and R3C7 in row 3 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 7 can be removed.
   R2C3 - removing <4> from <4568> leaving <568>
   R2C7 - removing <4> from <4568> leaving <568>
   R7C3 - removing <4> from <1456> leaving <156>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
   R3C3 - removing <8> from <458> leaving <45>
   R3C7 - removing <8> from <458> leaving <45>
   R9C3 - removing <8> from <1348> leaving <134>
   R9C7 - removing <8> from <148> leaving <14>
Squares R3C3 and R3C7 in row 3 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 row.
   R3C9 - removing <5> from <258> leaving <28>
R7C9 is the only square in column 9 that can be <5>
R7C3 is the only square in row 7 that can be <1>
Squares R1C7 (XY), R9C7 (XZ) and R2C8 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R7C8 - removing <4> from <46> leaving <6>
   R3C7 - removing <4> from <45> leaving <5>
R3C3 can only be <4>
R7C2 can only be <4>
R2C8 can only be <4>
R8C7 can only be <8>
R2C7 can only be <6>
R9C9 can only be <1>
R9C7 can only be <4>
R1C9 can only be <2>
R1C1 can only be <3>
R3C9 can only be <8>
R1C7 can only be <1>
R2C2 can only be <5>
R9C3 can only be <3>
R3C1 can only be <2>
R9C1 can only be <8>
R1C3 can only be <6>
R8C3 can only be <5>
R2C3 can only be <8>
R8C2 can only be <6>

[Puzzle Code = Sudoku-20190620-SuperHard-273836]

 

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