Aug 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <8>
R5C5 is the only square in row 5 that can be <9>
R8C5 is the only square in row 8 that can be <8>
R4C4 is the only square in row 4 that can be <8>
R9C2 is the only square in column 2 that can be <7>
R5C2 is the only square in column 2 that can be <6>
R8C3 is the only square in column 3 that can be <6>
R9C8 is the only square in column 8 that can be <6>
Intersection of column 6 with block 5. The values <27> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <7> from <567> leaving <56>
R6C5 - removing <7> from <167> leaving <16>
Squares R2C3 and R7C3 in column 3 and R2C5 and R7C5 in column 5 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 7 can be removed.
R2C1 - removing <4> from <1345> leaving <135>
R7C7 - removing <4> from <145> leaving <15>
R8C7 is the only square in column 7 that can be <4>
R8C1 can only be <5>
R8C9 can only be <2>
R7C2 can only be <3>
R3C2 can only be <5>
R1C8 is the only square in row 1 that can be <2>
R6C6 is the only square in row 6 that can be <2>
R5C7 is the only square in row 5 that can be <2>
R6C1 is the only square in row 6 that can be <7>
R4C1 can only be <3>
R2C1 can only be <1>
R5C3 can only be <1>
R4C6 is the only square in row 4 that can be <7>
Squares R2C9<35>, R4C9<56> and R6C9<36> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <356>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <5> from <159> leaving <19>
R9C9 - removing <5> from <159> leaving <19>
Intersection of row 1 with block 2. The value <5> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <5> from <457> leaving <47>
Intersection of row 9 with block 8. The value <5> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <5> from <145> leaving <14>
R4C5 is the only square in column 5 that can be <5>
R4C9 can only be <6>
R5C6 can only be <4>
R6C9 can only be <3>
R5C4 can only be <3>
R6C4 can only be <1>
R2C9 can only be <5>
R5C8 can only be <5>
R2C7 can only be <7>
R7C8 can only be <9>
R6C5 can only be <6>
R7C3 can only be <4>
R3C8 can only be <3>
R9C9 can only be <1>
R9C6 can only be <5>
R1C9 can only be <9>
R7C7 can only be <5>
R1C1 can only be <4>
R2C5 can only be <4>
R3C7 can only be <1>
R3C5 can only be <7>
R3C3 can only be <9>
R7C5 can only be <1>
R2C3 can only be <3>
R9C1 can only be <9>
R9C4 can only be <4>
R1C6 can only be <1>
R1C4 can only be <5>
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