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Sudoku Solution Path

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Puzzle Copyright © Kevin Stone

R2C9 is the only square in row 2 that can be <8>
R1C5 is the only square in row 1 that can be <8>
R1C1 is the only square in row 1 that can be <9>
R2C1 can only be <3>
R2C3 can only be <5>
R1C2 can only be <6>
R3C2 can only be <2>
R2C4 is the only square in row 2 that can be <9>
R3C8 is the only square in row 3 that can be <5>
R4C5 is the only square in row 4 that can be <1>
R5C3 is the only square in row 5 that can be <8>
R6C3 can only be <2>
R5C6 is the only square in row 5 that can be <2>
R6C8 is the only square in row 6 that can be <8>
R7C8 is the only square in row 7 that can be <2>
R7C5 is the only square in row 7 that can be <9>
R8C4 is the only square in row 8 that can be <1>
R8C1 is the only square in row 8 that can be <2>
R5C4 is the only square in column 4 that can be <7>
R2C6 is the only square in column 6 that can be <7>
R2C7 can only be <4>
Squares R5C5 and R6C5 in column 5 form a simple locked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C5 - removing <4> from <346> leaving <36>
   R9C5 - removing <45> from <3456> leaving <36>
Intersection of row 5 with block 6. The value <3> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
   R4C7 - removing <3> from <367> leaving <67>
   R4C8 - removing <3> from <347> leaving <47>
Intersection of column 7 with block 6. The values <67> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
   R4C8 - removing <7> from <47> leaving <4>
Squares R1C8, R1C9, R9C8 and R9C9 form a Type-1 Unique Rectangle on <37>.
   R9C9 - removing <37> from <3457> leaving <45>
R9C8 is the only square in row 9 that can be <7>
R1C8 can only be <3>
R1C9 can only be <7>
Intersection of block 9 with row 8. The value <3> only appears in one or more of squares R8C7, R8C8 and R8C9 of block 9. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
   R8C3 - removing <3> from <36> leaving <6>
R4C3 can only be <3>
R9C1 can only be <4>
R9C9 can only be <5>
R5C1 can only be <6>
R9C2 can only be <3>
R5C9 can only be <3>
R8C7 can only be <3>
R4C2 can only be <7>
R5C7 can only be <5>
R8C9 can only be <4>
R8C6 can only be <5>
R9C5 can only be <6>
R7C2 can only be <5>
R3C5 can only be <3>
R3C4 can only be <4>
R4C7 can only be <6>
R6C2 can only be <4>
R5C5 can only be <4>
R6C7 can only be <7>
R6C5 can only be <5>
R7C6 can only be <4>
R7C4 can only be <3>
R3C6 can only be <6>

[Puzzle Code = Sudoku-20200603-VeryHard-098298]

 

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