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Sudoku Solution Path

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Copyright © Kevin Stone

R2C7 is the only square in row 2 that can be <7>
R3C2 is the only square in row 3 that can be <7>
R3C3 is the only square in row 3 that can be <4>
R3C4 is the only square in row 3 that can be <8>
R8C4 can only be <7>
R9C8 is the only square in row 9 that can be <7>
R2C4 is the only square in column 4 that can be <9>
Intersection of row 2 with block 2. The value <1> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R3C6 - removing <1> from <156> leaving <56>
Intersection of column 1 with block 1. The value <3> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R1C2 - removing <3> from <356> leaving <56>
Intersection of column 1 with block 7. The value <8> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
   R8C3 - removing <8> from <589> leaving <59>
Intersection of column 4 with block 5. The value <5> 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.
   R4C6 - removing <5> from <245> leaving <24>
   R6C6 - removing <5> from <1256> leaving <126>
Intersection of column 8 with block 3. The value <5> 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 <5> from <2569> leaving <269>
   R2C9 - removing <5> from <256> leaving <26>
Squares R5C1<12>, R5C2<19> and R5C8<29> in row 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <129>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C5 - removing <1> from <146> leaving <46>
   R5C9 - removing <29> from <2469> leaving <46>
R2C5 is the only square in column 5 that can be <1>
R6C6 is the only square in column 6 that can be <1>
Intersection of column 9 with block 3. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R1C8 - removing <2> from <259> leaving <59>
Squares R1C2, R1C5 and R1C9 in row 1, R5C5 and R5C9 in row 5 and R9C2 and R9C5 in row 9 form a Swordfish pattern on possibility <6>. All other instances of this possibility in columns 2, 5 and 9 can be removed.
   R2C9 - removing <6> from <26> leaving <2>
   R7C2 - removing <6> from <1469> leaving <149>
R1C1 is the only square in row 1 that can be <2>
R5C1 can only be <1>
R5C2 can only be <9>
R5C8 can only be <2>
R1C5 is the only square in row 1 that can be <3>
R2C1 is the only square in row 2 that can be <3>
R8C7 is the only square in row 8 that can be <1>
R3C7 can only be <6>
R3C6 can only be <5>
R6C7 can only be <3>
R1C9 can only be <9>
R6C2 can only be <5>
R6C8 can only be <8>
R4C8 can only be <9>
R1C8 can only be <5>
R3C8 can only be <1>
R2C6 can only be <6>
R4C7 can only be <4>
R7C8 can only be <3>
R6C3 can only be <2>
R1C2 can only be <6>
R4C2 can only be <3>
R6C4 can only be <6>
R4C3 can only be <8>
R7C4 can only be <2>
R5C5 can only be <4>
R4C4 can only be <5>
R9C2 can only be <4>
R2C3 can only be <5>
R8C3 can only be <9>
R7C6 can only be <4>
R4C6 can only be <2>
R7C7 can only be <9>
R5C9 can only be <6>
R8C5 can only be <8>
R7C2 can only be <1>
R8C6 can only be <3>
R7C3 can only be <6>
R8C1 can only be <5>
R9C5 can only be <6>
R9C9 can only be <5>
R9C1 can only be <8>
R8C9 can only be <4>

[Puzzle Code = Sudoku-20191019-VeryHard-212211]

 

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