Oct 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <5>
R1C6 is the only square in row 1 that can be <3>
R2C6 can only be <6>
R2C5 can only be <5>
R3C5 can only be <2>
R3C4 can only be <9>
R5C5 can only be <4>
R2C3 is the only square in row 2 that can be <4>
R3C7 is the only square in row 3 that can be <5>
R4C9 is the only square in row 4 that can be <4>
R1C9 can only be <6>
R1C8 can only be <4>
R5C2 is the only square in row 5 that can be <9>
R6C4 is the only square in row 6 that can be <5>
R7C1 is the only square in row 7 that can be <5>
R8C9 is the only square in row 8 that can be <9>
R7C6 is the only square in row 7 that can be <9>
R9C1 is the only square in row 9 that can be <9>
R2C2 is the only square in column 2 that can be <1>
R5C4 is the only square in column 4 that can be <8>
R2C7 is the only square in column 7 that can be <3>
R2C1 can only be <8>
R7C7 is the only square in column 7 that can be <8>
R4C4 is the only square in block 5 that can be <6>
Intersection of row 7 with block 7. The value <2> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <2> from <2367> leaving <367>
R9C2 - removing <2> from <236> leaving <36>
Intersection of column 1 with block 4. The value <7> 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.
R6C3 - removing <7> from <267> leaving <26>
Intersection of column 2 with block 7. The value <6> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <6> from <267> leaving <27>
R8C3 - removing <6> from <367> leaving <37>
Squares R3C8, R3C9, R6C8 and R6C9 form a Type-3 Unique Rectangle on <18>. Upon close inspection, it is clear that:
(R6C8 or R6C9)<27> and R5C8<27> form a naked pair on <27> in block 6. No other squares in the block can contain these possibilities
R4C7 - removing <2> from <12> leaving <1>
(R6C8 or R6C9)<27>, R6C3<26> and R6C1<67> form a naked triplet on <267> in row 6. No other squares in the row can contain these possibilities
R6C6 - removing <27> from <127> leaving <1>
R8C7 can only be <2>
R8C4 can only be <3>
R9C8 can only be <6>
R9C2 can only be <3>
R8C3 can only be <7>
R9C4 can only be <2>
R4C2 can only be <2>
R4C6 can only be <7>
R7C2 can only be <6>
R6C3 can only be <6>
R4C1 can only be <3>
R5C6 can only be <2>
R5C8 can only be <7>
R8C8 can only be <1>
R6C9 can only be <8>
R6C1 can only be <7>
R3C3 can only be <3>
R6C8 can only be <2>
R3C9 can only be <1>
R7C5 can only be <1>
R7C9 can only be <7>
R8C5 can only be <6>
R7C3 can only be <2>
R3C8 can only be <8>
R3C1 can only be <6>
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