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Sudoku Solution Path

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Copyright © Kevin Stone

R1C5 can only be <7>
R4C3 can only be <1>
R6C3 can only be <4>
R5C1 can only be <3>
R5C4 can only be <4>
R5C9 can only be <8>
R7C4 can only be <3>
R5C5 can only be <9>
R5C6 can only be <1>
R3C4 can only be <6>
R9C5 can only be <8>
R4C5 can only be <3>
R7C6 can only be <4>
R3C6 can only be <3>
R4C4 can only be <7>
R6C4 can only be <2>
R6C6 can only be <6>
R4C7 can only be <6>
R6C5 can only be <5>
R4C6 can only be <8>
R6C7 can only be <3>
R1C8 is the only square in row 1 that can be <9>
R3C2 is the only square in row 3 that can be <5>
R7C3 is the only square in row 7 that can be <9>
R9C8 is the only square in row 9 that can be <2>
R3C7 is the only square in row 3 that can be <2>
R2C2 is the only square in row 2 that can be <2>
R8C7 is the only square in column 7 that can be <4>
Squares R3C8 and R7C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C8 - removing <78> from <3678> leaving <36>
   R8C8 - removing <78> from <3678> leaving <36>
Squares R8C8 and R9C9 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C9 - removing <36> from <1367> leaving <17>
Intersection of column 2 with block 7. The values <37> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
   R8C3 - removing <7> from <678> leaving <68>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 9 can be removed.
   R2C1 - removing <6> from <168> leaving <18>
   R2C9 - removing <6> from <1367> leaving <137>
   R8C1 - removing <6> from <168> leaving <18>
Squares R2C1 and R2C7 in row 2 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.
   R2C3 - removing <8> from <678> leaving <67>
   R2C9 - removing <1> from <137> leaving <37>
Squares R2C1 and R8C1 in column 1 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 column.
   R1C1 - removing <1> from <146> leaving <46>
Squares R7C7 and R8C1 form a remote locked pair. <18> can be removed from any square that is common to their groups.
   R8C9 - removing <1> from <17> leaving <7>
   R7C2 - removing <1> from <17> leaving <7>
R7C8 can only be <8>
R7C7 can only be <1>
R3C8 can only be <7>
R2C9 can only be <3>
R2C8 can only be <6>
R9C9 can only be <6>
R3C3 can only be <8>
R2C7 can only be <8>
R9C1 can only be <4>
R1C9 can only be <1>
R8C8 can only be <3>
R1C2 can only be <4>
R2C1 can only be <1>
R2C3 can only be <7>
R8C3 can only be <6>
R8C2 can only be <1>
R9C2 can only be <3>
R1C1 can only be <6>
R8C1 can only be <8>

[Puzzle Code = Sudoku-20191206-VeryHard-217998]

 

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