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Sudoku Solution Path

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Copyright © Kevin Stone

R8C2 can only be <8>
R1C9 is the only square in row 1 that can be <6>
R2C2 is the only square in row 2 that can be <4>
R2C8 is the only square in row 2 that can be <8>
R7C9 is the only square in row 7 that can be <5>
R5C2 is the only square in column 2 that can be <5>
Intersection of row 5 with block 5. The values <26> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
   R4C4 - removing <6> from <568> leaving <58>
   R4C5 - removing <6> from <34567> leaving <3457>
   R6C4 - removing <26> from <2689> leaving <89>
   R6C5 - removing <26> from <24679> leaving <479>
   R6C6 - removing <2> from <12489> leaving <1489>
R5C4 is the only square in column 4 that can be <6>
Intersection of row 7 with block 7. The values <13> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
   R8C1 - removing <3> from <369> leaving <69>
   R9C1 - removing <1> from <1269> leaving <269>
   R9C2 - removing <1> from <12> leaving <2>
R1C2 can only be <1>
R2C9 is the only square in row 2 that can be <1>
R9C8 is the only square in row 9 that can be <1>
R3C9 is the only square in column 9 that can be <2>
R3C3 can only be <3>
R7C3 can only be <1>
R4C3 can only be <6>
R6C3 can only be <2>
R6C7 is the only square in row 6 that can be <6>
R7C1 is the only square in row 7 that can be <3>
R7C4 is the only square in column 4 that can be <2>
R5C6 is the only square in column 6 that can be <2>
Squares R8C1 and R8C5 in row 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R8C8 - removing <9> from <379> leaving <37>
   R8C9 - removing <9> from <379> leaving <37>
Squares R1C5 and R1C8 in row 1 and R5C5 and R5C8 in row 5 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 5 and 8 can be removed.
   R6C5 - removing <9> from <479> leaving <47>
   R8C5 - removing <9> from <69> leaving <6>
   R9C5 - removing <9> from <469> leaving <46>
R8C1 can only be <9>
R9C5 can only be <4>
R9C9 can only be <9>
R6C5 can only be <7>
R7C6 can only be <9>
R9C1 can only be <6>
R7C7 can only be <4>
R6C9 can only be <4>
R4C7 can only be <7>
R3C6 can only be <8>
R6C6 can only be <1>
R4C9 can only be <3>
R3C7 can only be <9>
R4C5 can only be <5>
R8C9 can only be <7>
R5C8 can only be <9>
R5C5 can only be <3>
R1C8 can only be <7>
R6C1 can only be <8>
R4C6 can only be <4>
R8C8 can only be <3>
R1C1 can only be <2>
R3C4 can only be <5>
R4C4 can only be <8>
R2C5 can only be <2>
R6C4 can only be <9>
R4C1 can only be <1>
R1C5 can only be <9>
R2C1 can only be <5>
R3C1 can only be <7>

[Puzzle Code = Sudoku-20191023-VeryHard-024725]

 

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