Aug 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <7>
R6C6 can only be <4>
R5C5 can only be <3>
R1C5 can only be <4>
R9C5 can only be <6>
R7C5 can only be <7>
R7C4 can only be <5>
R3C5 can only be <9>
R9C4 can only be <3>
R2C4 can only be <6>
R8C6 can only be <8>
R1C1 is the only square in row 1 that can be <5>
R1C9 is the only square in row 1 that can be <7>
R6C8 is the only square in row 6 that can be <9>
R9C7 is the only square in column 7 that can be <5>
Squares R1C3 and R2C3 in block 1 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 block.
R2C1 - removing <1> from <1249> leaving <249>
R2C2 - removing <1> from <1249> leaving <249>
Squares R8C7<36>, R8C8<136> and R8C9<16> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <136>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <16> from <1679> leaving <79>
R8C2 - removing <1> from <179> leaving <79>
Intersection of row 8 with block 9. The values <136> 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 these values.
R7C8 - removing <6> from <268> leaving <28>
R9C9 - removing <1> from <128> leaving <28>
Squares R1C3, R2C3, R1C8 and R2C8 form a Type-3 Unique Rectangle on <13>. Upon close inspection, it is clear that:
(R1C8 or R2C8)<24>, R7C8<28> and R5C8<48> form a naked triplet on <248> in column 8. No other squares in the column can contain these possibilities
R4C8 - removing <24> from <246> leaving <6>
(R1C8 or R2C8)<24>, R7C8<28>, R5C8<48> and R4C8<246> form a naked quad on <2468> in column 8. No other squares in the column can contain these possibilities
R8C8 - removing <6> from <136> leaving <13>
R4C7 can only be <2>
R6C3 is the only square in row 6 that can be <6>
R7C3 can only be <8>
R7C8 can only be <2>
R7C1 can only be <6>
R9C9 can only be <8>
R6C9 can only be <5>
R6C2 can only be <8>
R5C9 can only be <4>
R5C1 can only be <7>
R5C8 can only be <8>
R5C2 can only be <5>
R8C1 can only be <9>
R8C2 can only be <7>
R1C6 is the only square in row 1 that can be <2>
R3C6 can only be <3>
R3C7 can only be <6>
R3C9 can only be <2>
R8C7 can only be <3>
R3C2 can only be <4>
R2C9 can only be <1>
R8C8 can only be <1>
R8C9 can only be <6>
R1C8 can only be <3>
R1C3 can only be <1>
R2C8 can only be <4>
R2C1 can only be <2>
R2C3 can only be <3>
R4C2 can only be <1>
R4C1 can only be <4>
R9C2 can only be <2>
R9C1 can only be <1>
R2C2 can only be <9>
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