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Sudoku Solution Path

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Copyright © Kevin Stone

R8C5 can only be <9>
R3C5 is the only square in row 3 that can be <2>
R2C5 is the only square in column 5 that can be <4>
Squares R1C1 and R1C9 in row 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C4 - removing <7> from <789> leaving <89>
   R1C6 - removing <7> from <789> leaving <89>
Squares R1C4 and R1C6 in block 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R3C4 - removing <9> from <379> leaving <37>
   R3C6 - removing <9> from <379> leaving <37>
Squares R3C4 and R3C6 in row 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C2 - removing <7> from <17> leaving <1>
   R3C7 - removing <7> from <4679> leaving <469>
   R3C8 - removing <7> from <467> leaving <46>
R8C2 can only be <5>
R7C2 can only be <3>
R7C5 can only be <8>
R5C5 can only be <3>
Intersection of row 8 with block 9. The value <7> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R7C7 - removing <7> from <4567> leaving <456>
   R7C8 - removing <7> from <14567> leaving <1456>
Intersection of column 1 with block 4. The value <6> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
   R4C3 - removing <6> from <3568> leaving <358>
   R6C3 - removing <6> from <13568> leaving <1358>
Squares R3C6<37>, R7C6<57> and R9C6<35> in column 6 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R4C6 - removing <5> from <5689> leaving <689>
   R6C6 - removing <5> from <568> leaving <68>
Intersection of column 6 with block 8. The value <5> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
   R7C4 - removing <5> from <157> leaving <17>
   R9C4 - removing <5> from <135> leaving <13>
Squares R5C3 and R5C8 in row 5 and R8C3 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 8 can be removed.
   R6C3 - removing <1> from <1358> leaving <358>
   R7C3 - removing <1> from <146> leaving <46>
   R7C8 - removing <1> from <1456> leaving <456>
R7C4 is the only square in row 7 that can be <1>
R9C4 can only be <3>
R9C6 can only be <5>
R3C4 can only be <7>
R7C6 can only be <7>
R3C6 can only be <3>
Intersection of column 9 with block 6. The value <5> 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.
   R4C7 - removing <5> from <3578> leaving <378>
   R5C7 - removing <5> from <578> leaving <78>
   R5C8 - removing <5> from <157> leaving <17>
   R6C7 - removing <5> from <3458> leaving <348>
R5C3 is the only square in row 5 that can be <5>
R5C8 is the only square in row 5 that can be <1>
R6C1 is the only square in row 6 that can be <1>
R9C1 can only be <4>
R9C9 can only be <1>
R1C1 can only be <7>
R7C3 can only be <6>
R1C9 can only be <4>
R4C1 can only be <6>
R2C2 can only be <8>
R6C9 can only be <5>
R3C8 can only be <6>
R2C3 can only be <9>
R5C2 can only be <7>
R3C3 can only be <4>
R3C7 can only be <9>
R8C8 can only be <7>
R5C7 can only be <8>
R6C4 can only be <8>
R4C9 can only be <7>
R8C3 can only be <1>
R8C7 can only be <6>
R2C8 can only be <5>
R2C7 can only be <7>
R7C8 can only be <4>
R4C7 can only be <3>
R6C3 can only be <3>
R6C6 can only be <6>
R1C4 can only be <9>
R4C6 can only be <9>
R7C7 can only be <5>
R1C6 can only be <8>
R4C4 can only be <5>
R4C3 can only be <8>
R6C7 can only be <4>

[Puzzle Code = Sudoku-20190625-VeryHard-161945]

 

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