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Sudoku Solution Path

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Copyright © Kevin Stone

R5C7 can only be <1>
R1C3 is the only square in row 1 that can be <2>
R3C3 can only be <3>
R3C7 can only be <5>
R2C2 is the only square in row 2 that can be <6>
R3C5 is the only square in row 3 that can be <2>
R6C5 can only be <7>
R6C8 can only be <3>
R4C8 can only be <7>
R2C9 is the only square in row 2 that can be <7>
R4C4 is the only square in row 4 that can be <3>
R5C5 is the only square in row 5 that can be <6>
R7C1 is the only square in row 7 that can be <5>
R8C8 is the only square in row 8 that can be <5>
R9C9 is the only square in row 9 that can be <2>
R9C7 is the only square in row 9 that can be <6>
R9C3 is the only square in row 9 that can be <7>
R8C1 is the only square in column 1 that can be <3>
Squares R2C4 and R2C6 in row 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R2C1 - removing <14> from <1489> leaving <89>
   R2C8 - removing <1> from <189> leaving <89>
Intersection of column 1 with block 1. The value <8> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R1C2 - removing <8> from <1489> leaving <149>
Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R1C9 - removing <8> from <1348> leaving <134>
Squares R2C1, R2C8, R1C1 and R1C8 form a Type-4 Unique Rectangle on <89>.
   R1C1 - removing <9> from <1489> leaving <148>
   R1C8 - removing <9> from <189> leaving <18>
Squares R2C1 and R9C1 in column 1 and R2C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 2 and 9 can be removed.
   R9C2 - removing <9> from <149> leaving <14>
Squares R5C6 (XY), R2C6 (XZ) and R4C5 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
   R4C6 - removing <1> from <159> leaving <59>
R4C5 is the only square in row 4 that can be <1>
R7C5 can only be <9>
R7C3 can only be <8>
R7C7 can only be <3>
R1C7 can only be <9>
R2C8 can only be <8>
R2C1 can only be <9>
R1C8 can only be <1>
R7C9 can only be <1>
R5C3 can only be <9>
R3C9 can only be <4>
R8C9 can only be <8>
R9C8 can only be <9>
R1C2 can only be <4>
R3C1 can only be <1>
R1C9 can only be <3>
R5C6 can only be <4>
R4C2 can only be <5>
R5C4 can only be <8>
R2C6 can only be <1>
R1C1 can only be <8>
R9C2 can only be <1>
R2C4 can only be <4>
R8C6 can only be <2>
R9C1 can only be <4>
R4C6 can only be <9>
R6C2 can only be <8>
R6C4 can only be <2>
R6C6 can only be <5>
R8C4 can only be <1>
R8C2 can only be <9>

 

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