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Sudoku Solution Path

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Copyright © Kevin Stone

R1C1 is the only square in row 1 that can be <3>
R4C6 is the only square in row 4 that can be <4>
R4C4 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <2>
R6C1 is the only square in row 6 that can be <2>
R8C1 can only be <5>
R8C8 can only be <9>
R8C2 can only be <2>
R8C9 can only be <7>
R6C4 is the only square in row 6 that can be <6>
R7C3 is the only square in row 7 that can be <9>
R3C7 is the only square in column 7 that can be <6>
Squares R1C3, R1C4 and R1C6 in row 1 form a simple locked triplet. These 3 squares all contain the 3 possibilities <157>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C7 - removing <1> from <128> leaving <28>
   R1C8 - removing <15> from <158> leaving <8>
   R1C9 - removing <15> from <124589> leaving <2489>
R1C7 can only be <2>
R9C9 is the only square in row 9 that can be <2>
Squares R7C1 and R9C3 in block 7 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.
   R9C1 - removing <18> from <1468> leaving <46>
Intersection of row 2 with block 3. The value <5> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R3C9 - removing <5> from <145> leaving <14>
Intersection of block 2 with row 1. The value <1> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
   R1C3 - removing <1> from <157> leaving <57>
Squares R5C6 and R5C7 in row 5 and R9C6 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 6 and 7 can be removed.
   R7C7 - removing <3> from <138> leaving <18>
Squares R7C1 and R7C7 in row 7 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.
   R7C9 - removing <18> from <1358> leaving <35>
Intersection of column 9 with block 6. The value <8> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
   R5C7 - removing <8> from <138> leaving <13>
R5C3 is the only square in row 5 that can be <8>
R9C3 can only be <1>
R4C1 can only be <7>
R9C8 can only be <5>
R7C1 can only be <8>
R9C4 can only be <7>
R2C8 can only be <1>
R7C9 can only be <3>
R2C1 can only be <6>
R3C9 can only be <4>
R1C9 can only be <9>
R3C1 can only be <1>
R7C7 can only be <1>
R5C7 can only be <3>
R7C5 can only be <5>
R4C9 can only be <8>
R9C7 can only be <8>
R9C6 can only be <3>
R5C4 can only be <1>
R1C2 can only be <4>
R2C9 can only be <5>
R2C2 can only be <9>
R9C1 can only be <4>
R4C5 can only be <3>
R6C9 can only be <1>
R5C6 can only be <7>
R1C4 can only be <5>
R6C6 can only be <5>
R6C5 can only be <8>
R1C6 can only be <1>
R3C5 can only be <7>
R9C2 can only be <6>
R1C3 can only be <7>
R3C3 can only be <5>

[Puzzle Code = Sudoku-20190916-VeryHard-302732]

 

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