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Sudoku Solution Path

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Sudoku Puzzle © Kevin Stone

R4C2 is the only square in row 4 that can be <5>
R4C1 is the only square in row 4 that can be <7>
R7C8 is the only square in row 7 that can be <7>
R7C2 is the only square in row 7 that can be <8>
R8C2 can only be <2>
R8C3 is the only square in row 8 that can be <5>
R9C5 is the only square in row 9 that can be <5>
R5C1 is the only square in column 1 that can be <2>
R8C8 is the only square in column 8 that can be <8>
R8C4 can only be <6>
R8C6 can only be <4>
R8C7 can only be <9>
Squares R5C4<17>, R5C6<167> and R5C7<16> in row 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <167>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C3 - removing <1> from <139> leaving <39>
   R5C9 - removing <6> from <369> leaving <39>
Intersection of block 4 with row 6. The value <1> only appears in one or more of squares R6C1, R6C2 and R6C3 of block 4. These squares are the ones that intersect with row 6. Thus, the other (non-intersecting) squares of row 6 cannot contain this value.
   R6C5 - removing <1> from <136> leaving <36>
   R6C8 - removing <1> from <149> leaving <49>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.
   R6C9 - removing <4> from <3469> leaving <369>
R6C8 is the only square in row 6 that can be <4>
Intersection of column 8 with block 3. The value <9> 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 <9> from <469> leaving <46>
Squares R6C2 (XY), R3C2 (XZ) and R6C5 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
   R3C5 - removing <6> from <1269> leaving <129>
Squares R1C5 and R6C5 in column 5 and R1C9 and R6C9 in column 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 6 can be removed.
   R1C6 - removing <6> from <168> leaving <18>
Squares R1C4 and R1C6 in row 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C1 - removing <1> from <149> leaving <49>
   R1C5 - removing <1> from <169> leaving <69>
Squares R1C6 and R9C6 in column 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C6 - removing <1> from <167> leaving <67>
   R5C6 - removing <1> from <167> leaving <67>
Squares R1C4 and R1C6 in block 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R2C4 - removing <1> from <127> leaving <27>
   R3C5 - removing <1> from <129> leaving <29>
Squares R1C4, R1C6, R9C4 and R9C6 form a Type-1 Unique Rectangle on <18>.
   R9C4 - removing <18> from <128> leaving <2>
R9C9 can only be <4>
R2C4 can only be <7>
R7C5 can only be <1>
R9C1 can only be <1>
R1C9 can only be <6>
R7C7 can only be <2>
R1C5 can only be <9>
R2C6 can only be <6>
R5C4 can only be <1>
R5C6 can only be <7>
R5C7 can only be <6>
R1C4 can only be <8>
R4C5 can only be <3>
R7C3 can only be <4>
R9C6 can only be <8>
R2C7 can only be <1>
R6C1 can only be <9>
R1C6 can only be <1>
R1C1 can only be <4>
R3C5 can only be <2>
R2C2 can only be <3>
R3C7 can only be <4>
R3C8 can only be <9>
R3C3 can only be <1>
R2C8 can only be <2>
R4C9 can only be <2>
R6C5 can only be <6>
R4C8 can only be <1>
R6C9 can only be <3>
R5C3 can only be <3>
R6C2 can only be <1>
R5C9 can only be <9>
R2C3 can only be <9>
R3C2 can only be <6>

 

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