Aug 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <9>
R3C1 is the only square in row 3 that can be <4>
R6C6 is the only square in row 6 that can be <9>
R6C4 is the only square in row 6 that can be <6>
R1C6 is the only square in row 1 that can be <6>
R7C1 is the only square in row 7 that can be <9>
R8C9 is the only square in row 8 that can be <6>
R8C5 is the only square in row 8 that can be <9>
R9C8 is the only square in row 9 that can be <4>
R9C6 is the only square in row 9 that can be <5>
R2C6 is the only square in column 6 that can be <2>
Squares R2C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C1 - removing <3> from <2357> leaving <257>
R5C1 - removing <38> from <238> leaving <2>
R6C1 - removing <8> from <578> leaving <57>
R4C9 is the only square in row 4 that can be <2>
R4C4 is the only square in row 4 that can be <4>
R1C5 is the only square in row 1 that can be <4>
R5C9 is the only square in row 5 that can be <4>
R9C2 is the only square in column 2 that can be <2>
Squares R4C2 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C8 - removing <1> from <157> leaving <57>
Intersection of row 3 with block 3. The value <1> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <1> from <1378> leaving <378>
Intersection of row 7 with block 9. The value <7> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <7> from <178> leaving <18>
Intersection of row 8 with block 8. The value <1> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C4 - removing <1> from <1378> leaving <378>
R9C5 - removing <1> from <137> leaving <37>
Intersection of column 8 with block 6. The values <15> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R6C9 - removing <1> from <178> leaving <78>
Squares R4C1, R4C8, R6C1 and R6C8 form a Type-1 Unique Rectangle on <57>.
R6C8 - removing <57> from <1578> leaving <18>
R6C1 is the only square in row 6 that can be <5>
R4C1 can only be <7>
R4C8 can only be <5>
R6C9 is the only square in row 6 that can be <7>
R7C7 is the only square in row 7 that can be <7>
R1C8 is the only square in column 8 that can be <7>
R1C4 can only be <3>
Squares R6C2, R6C8, R5C2 and R5C8 form a Type-1 Unique Rectangle on <18>.
R5C2 - removing <18> from <138> leaving <3>
R5C5 can only be <1>
R4C2 can only be <1>
R5C8 can only be <8>
R2C5 can only be <7>
R4C6 can only be <3>
R6C8 can only be <1>
R6C2 can only be <8>
R2C4 can only be <1>
R9C5 can only be <3>
R8C6 can only be <1>
R8C4 can only be <8>
R8C1 can only be <3>
R9C4 can only be <7>
R2C1 can only be <8>
R2C9 can only be <3>
R1C3 can only be <2>
R3C9 can only be <1>
R3C7 can only be <2>
R7C9 can only be <8>
R7C3 can only be <1>
R9C7 can only be <1>
R9C3 can only be <8>
R1C7 can only be <8>
R3C3 can only be <3>
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