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Sudoku Solution Path

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Sudoku Puzzle © Kevin Stone

R2C2 can only be <2>
R7C3 can only be <4>
R8C5 can only be <4>
R8C8 can only be <5>
R8C2 can only be <7>
R5C2 can only be <4>
R9C3 can only be <8>
R1C3 can only be <1>
R3C3 can only be <5>
R5C3 can only be <7>
R4C1 can only be <6>
R4C6 can only be <4>
R6C1 can only be <5>
R6C5 is the only square in row 6 that can be <1>
R6C6 is the only square in row 6 that can be <9>
R9C1 is the only square in row 9 that can be <9>
R7C1 can only be <3>
R7C5 is the only square in row 7 that can be <9>
Squares R9C4 and R9C6 in row 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R9C7 - removing <6> from <367> leaving <37>
   R9C9 - removing <6> from <367> leaving <37>
Squares R6C9 and R7C9 in column 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R1C9 - removing <6> from <4678> leaving <478>
Intersection of column 4 with block 5. The value <3> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
   R4C5 - removing <3> from <378> leaving <78>
   R5C5 - removing <3> from <368> leaving <68>
Squares R2C5 and R5C5 in column 5 and R2C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 2 and 5 can be removed.
   R5C4 - removing <6> from <2356> leaving <235>
   R5C6 - removing <6> from <256> leaving <25>
   R5C7 - removing <6> from <2368> leaving <238>
Squares R1C1, R3C1, R1C9 and R3C9 form a Type-3 Unique Rectangle on <48>. Upon close inspection, it is clear that:
(R1C9 or R3C9)<37> and R9C9<37> form a locked pair on <37> in column 9. No other squares in the column can contain these possibilities
   R4C9 - removing <3> from <38> leaving <8>
R4C5 can only be <7>
R4C4 can only be <3>
R3C5 can only be <3>
R2C5 can only be <6>
R2C8 can only be <3>
R5C5 can only be <8>
R1C6 can only be <2>
R5C8 can only be <6>
R6C9 can only be <2>
R6C4 can only be <6>
R7C9 can only be <6>
R5C7 can only be <3>
R7C7 can only be <2>
R1C4 can only be <7>
R5C6 can only be <5>
R5C4 can only be <2>
R9C6 can only be <6>
R9C7 can only be <7>
R9C4 can only be <5>
R9C9 can only be <3>
R3C7 can only be <8>
R1C9 can only be <4>
R1C1 can only be <8>
R3C9 can only be <7>
R3C1 can only be <4>
R1C7 can only be <6>

 

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