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Sudoku Solution Path

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Copyright © Kevin Stone

R7C6 can only be <4>
R7C4 can only be <1>
R7C1 can only be <7>
R7C5 can only be <2>
R3C4 can only be <6>
R8C4 can only be <8>
R7C9 can only be <3>
R2C2 is the only square in row 2 that can be <2>
R5C8 is the only square in row 5 that can be <2>
R6C1 is the only square in row 6 that can be <2>
R8C7 is the only square in row 8 that can be <7>
R8C8 is the only square in row 8 that can be <5>
R4C1 is the only square in column 1 that can be <5>
R1C2 is the only square in column 2 that can be <9>
R8C6 is the only square in column 6 that can be <6>
R8C5 can only be <9>
Squares R9C8 and R9C9 in row 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R9C1 - removing <1> from <168> leaving <68>
   R9C2 - removing <1> from <168> leaving <68>
Squares R1C9 and R9C9 in column 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C9 - removing <1> from <189> leaving <89>
   R4C9 - removing <14> from <1479> leaving <79>
   R6C9 - removing <4> from <478> leaving <78>
Intersection of row 1 with block 3. The value <4> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R2C7 - removing <4> from <148> leaving <18>
   R2C8 - removing <4> from <1469> leaving <169>
Intersection of column 1 with block 1. The value <1> 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.
   R2C3 - removing <1> from <168> leaving <68>
Intersection of column 7 with block 6. The values <45> 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 <4> from <1349> leaving <139>
   R6C8 - removing <4> from <34> leaving <3>
Intersection of block 5 with row 5. The value <7> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
   R5C2 - removing <7> from <1378> leaving <138>
Squares R9C8, R9C9, R1C8 and R1C9 form a Type-1 Unique Rectangle on <14>.
   R1C8 - removing <14> from <146> leaving <6>
R1C1 can only be <1>
R1C9 can only be <4>
R3C1 can only be <8>
R9C9 can only be <1>
R3C9 can only be <9>
R9C1 can only be <6>
R2C3 can only be <6>
R3C6 can only be <3>
R4C9 can only be <7>
R2C8 can only be <1>
R6C9 can only be <8>
R9C2 can only be <8>
R9C8 can only be <4>
R6C3 can only be <4>
R2C5 can only be <4>
R2C7 can only be <8>
R4C8 can only be <9>
R3C5 can only be <1>
R5C6 can only be <7>
R5C4 can only be <4>
R2C6 can only be <9>
R6C7 can only be <5>
R6C5 can only be <6>
R2C4 can only be <7>
R5C7 can only be <1>
R5C2 can only be <3>
R4C7 can only be <4>
R6C2 can only be <7>
R4C5 can only be <3>
R4C3 can only be <1>
R5C5 can only be <5>
R5C3 can only be <8>
R8C2 can only be <1>
R8C3 can only be <3>
R4C2 can only be <6>

[Puzzle Code = Sudoku-20191021-VeryHard-024948]

 

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