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Sudoku Solution Path

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Copyright © Kevin Stone

R4C5 can only be <5>
R6C5 can only be <6>
R5C6 can only be <2>
R5C4 can only be <8>
R9C6 can only be <1>
R1C6 can only be <5>
R5C5 can only be <7>
R1C1 is the only square in row 1 that can be <7>
R9C9 is the only square in row 9 that can be <7>
R9C8 is the only square in row 9 that can be <4>
R5C8 can only be <9>
R1C8 can only be <8>
Squares R5C7 and R6C9 in block 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R5C9 - removing <15> from <1345> leaving <34>
Squares R1C4 and R9C4 in column 4 and R1C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 1 and 9 can be removed.
   R9C1 - removing <2> from <25689> leaving <5689>
   R1C5 - removing <2> from <1234> leaving <134>
   R9C5 - removing <2> from <2389> leaving <389>
   R1C9 - removing <2> from <1269> leaving <169>
Squares R6C1 and R6C9 in row 6 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
   R5C1 - removing <5> from <13456> leaving <1346>
   R9C1 - removing <5> from <5689> leaving <689>
Squares R4C1, R4C9, R5C1 and R5C9 form a Type-1 Unique Rectangle on <34>.
   R5C1 - removing <34> from <1346> leaving <16>
Squares R1C4 (XY), R1C7 (XZ) and R2C5 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
   R2C9 - removing <1> from <16> leaving <6>
   R1C5 - removing <1> from <134> leaving <34>
R2C1 can only be <3>
R2C5 can only be <1>
R4C1 can only be <4>
R4C9 can only be <3>
R3C1 can only be <9>
R5C9 can only be <4>
R3C9 can only be <2>
R1C2 can only be <6>
R3C5 can only be <4>
R7C9 can only be <8>
R1C7 can only be <1>
R7C1 can only be <2>
R8C9 can only be <5>
R6C9 can only be <1>
R9C7 can only be <2>
R9C4 can only be <3>
R1C3 can only be <4>
R5C2 can only be <3>
R9C2 can only be <9>
R1C5 can only be <3>
R1C4 can only be <2>
R1C9 can only be <9>
R5C7 can only be <5>
R5C3 can only be <6>
R6C1 can only be <5>
R7C5 can only be <9>
R8C1 can only be <8>
R9C5 can only be <8>
R8C5 can only be <2>
R9C1 can only be <6>
R9C3 can only be <5>
R5C1 can only be <1>

 

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