Oct 11 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <1>
R1C5 is the only square in row 1 that can be <5>
R1C3 is the only square in row 1 that can be <6>
R2C8 is the only square in row 2 that can be <8>
R5C6 is the only square in row 5 that can be <9>
R6C6 is the only square in row 6 that can be <6>
R8C3 is the only square in row 8 that can be <7>
R8C2 is the only square in row 8 that can be <2>
R2C3 is the only square in row 2 that can be <2>
R8C4 is the only square in row 8 that can be <8>
R6C5 is the only square in row 6 that can be <8>
R9C9 is the only square in row 9 that can be <9>
R7C9 can only be <8>
R7C2 is the only square in row 7 that can be <9>
R7C1 is the only square in block 7 that can be <5>
Squares R9C1 and R9C3 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <4> from <134> leaving <13>
R9C7 - removing <4> from <134> leaving <13>
Intersection of block 8 with column 5. The value <1> only appears in one or more of squares R7C5, R8C5 and R9C5 of block 8. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R3C5 - removing <1> from <147> leaving <47>
R4C5 - removing <1> from <1237> leaving <237>
R5C5 - removing <1> from <1234> leaving <234>
R3C2 is the only square in row 3 that can be <1>
Squares R5C1<348>, R5C3<48>, R5C5<234> and R5C9<23> in row 5 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <4> from <145> leaving <15>
R5C7 - removing <3> from <135> leaving <15>
Squares R3C1 and R5C1 in column 1 and R3C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 3 and 5 can be removed.
R5C5 - removing <3> from <234> leaving <24>
R3C8 - removing <3> from <234> leaving <24>
Intersection of block 5 with row 4. The values <37> only appears in one or more of squares R4C4, R4C5 and R4C6 of block 5. These squares are the ones that intersect with row 4. Thus, the other (non-intersecting) squares of row 4 cannot contain these values.
R4C2 - removing <3> from <35> leaving <5>
R4C8 - removing <3> from <1235> leaving <125>
Squares R3C8<24>, R4C8<12> and R7C8<14> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C8 - removing <4> from <345> leaving <35>
Squares R2C2 and R6C2 in column 2 and R2C4 and R6C4 in column 4 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 6 can be removed.
R2C6 - removing <4> from <14> leaving <1>
R2C7 - removing <4> from <347> leaving <37>
R4C6 can only be <3>
R8C6 can only be <4>
R7C5 can only be <1>
R7C8 can only be <4>
R9C5 can only be <3>
R3C8 can only be <2>
R9C7 can only be <1>
R5C7 can only be <5>
R3C9 can only be <3>
R4C8 can only be <1>
R5C9 can only be <2>
R2C7 can only be <7>
R4C4 can only be <7>
R5C4 can only be <1>
R8C7 can only be <3>
R6C8 can only be <3>
R5C5 can only be <4>
R6C2 can only be <4>
R8C8 can only be <5>
R2C4 can only be <4>
R1C7 can only be <4>
R4C5 can only be <2>
R5C3 can only be <8>
R3C5 can only be <7>
R6C4 can only be <5>
R2C2 can only be <3>
R1C1 can only be <7>
R3C1 can only be <4>
R5C1 can only be <3>
R9C3 can only be <4>
R9C1 can only be <8>
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