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Sudoku Solution Path

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Puzzle Copyright © Kevin Stone

R6C5 can only be <3>
R5C7 is the only square in row 5 that can be <3>
R5C5 is the only square in row 5 that can be <5>
R5C6 is the only square in row 5 that can be <1>
R5C3 is the only square in row 5 that can be <6>
Squares R5C1 and R5C9 in row 5 form a simple locked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C2 - removing <4> from <249> leaving <29>
   R5C8 - removing <4> from <479> leaving <79>
Squares R1C3<147>, R2C2<47>, R2C3<478> and R3C1<148> in block 1 form a comprehensive locked quad. These 4 squares can only contain the 4 possibilities <1478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R3C2 - removing <47> from <3479> leaving <39>
   R3C3 - removing <1478> from <134789> leaving <39>
Squares R1C3, R1C5 and R1C7 in row 1, R4C5 and R4C7 in row 4 and R9C3 and R9C5 in row 9 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
   R2C3 - removing <7> from <478> leaving <48>
   R2C5 - removing <7> from <24678> leaving <2468>
   R2C7 - removing <7> from <2467> leaving <246>
   R3C5 - removing <7> from <24678> leaving <2468>
   R3C7 - removing <7> from <124567> leaving <12456>
   R7C3 - removing <7> from <123457> leaving <12345>
   R7C5 - removing <7> from <12789> leaving <1289>
Squares R2C3 and R2C5 in row 2, R6C3 and R6C7 in row 6 and R8C5 and R8C7 in row 8 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
   R3C5 - removing <8> from <2468> leaving <246>
   R7C5 - removing <8> from <1289> leaving <129>
   R7C7 - removing <8> from <245689> leaving <24569>
Squares R4C5 (XY), R4C3 (XZ) and R1C5 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R1C3 - removing <4> from <147> leaving <17>
Squares R8C2 (XY), R9C3 (XZ) and R2C2 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
   R7C2 - removing <7> from <2347> leaving <234>
   R1C3 - removing <7> from <17> leaving <1>
R3C7 is the only square in row 3 that can be <1>
R3C8 is the only square in row 3 that can be <5>
R8C5 is the only square in row 8 that can be <1>
R7C1 is the only square in row 7 that can be <1>
R8C7 is the only square in row 8 that can be <8>
R6C7 can only be <9>
R6C3 can only be <8>
R9C7 can only be <2>
R5C8 can only be <7>
R9C3 can only be <7>
R8C8 can only be <4>
R5C4 can only be <2>
R4C7 can only be <4>
R2C3 can only be <4>
R5C1 can only be <4>
R8C2 can only be <2>
R2C8 can only be <2>
R7C8 can only be <9>
R7C9 can only be <6>
R9C5 can only be <9>
R7C5 can only be <2>
R2C2 can only be <7>
R2C7 can only be <6>
R4C3 can only be <2>
R3C1 can only be <8>
R7C7 can only be <5>
R3C9 can only be <4>
R2C5 can only be <8>
R5C9 can only be <8>
R1C7 can only be <7>
R4C5 can only be <7>
R8C3 can only be <5>
R5C2 can only be <9>
R1C5 can only be <4>
R3C2 can only be <3>
R3C4 can only be <7>
R7C6 can only be <7>
R3C5 can only be <6>
R7C4 can only be <8>
R3C6 can only be <2>
R7C3 can only be <3>
R3C3 can only be <9>
R7C2 can only be <4>

[Puzzle Code = Sudoku-20200603-SuperHard-133162]

 

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