Sep 14 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 is the only square in row 5 that can be <6>
R9C2 is the only square in row 9 that can be <6>
R7C2 is the only square in column 2 that can be <5>
R7C7 can only be <3>
R7C3 is the only square in row 7 that can be <2>
R9C5 is the only square in row 9 that can be <3>
R3C7 is the only square in column 7 that can be <2>
R3C8 is the only square in column 8 that can be <3>
R3C4 is the only square in row 3 that can be <5>
R6C8 is the only square in column 8 that can be <5>
R5C9 can only be <1>
R5C5 can only be <5>
R1C8 is the only square in column 8 that can be <1>
R3C2 is the only square in column 2 that can be <1>
R3C3 can only be <4>
R3C6 can only be <7>
R8C3 is the only square in column 3 that can be <1>
R4C5 is the only square in column 5 that can be <1>
R4C8 is the only square in block 6 that can be <9>
R7C8 can only be <8>
R9C8 can only be <4>
R9C9 can only be <9>
R9C1 can only be <8>
R8C1 can only be <9>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <4> from <457> leaving <57>
Intersection of column 1 with block 1. The value <7> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <7> from <278> leaving <28>
Squares R6C3<68>, R6C5<48> and R6C7<46> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <8> from <278> leaving <27>
R6C4 - removing <48> from <4789> leaving <79>
R6C6 - removing <48> from <2489> leaving <29>
Squares R8C7, R8C9, R2C7 and R2C9 form a Type-1 Unique Rectangle on <57>.
R2C9 - removing <57> from <457> leaving <4>
R1C9 can only be <7>
R1C1 can only be <2>
R8C9 can only be <5>
R2C7 can only be <5>
R8C7 can only be <7>
R1C2 can only be <8>
R5C1 can only be <3>
R1C5 can only be <4>
R4C2 can only be <7>
R2C3 can only be <3>
R6C5 can only be <8>
R2C1 can only be <7>
R6C2 can only be <2>
R5C6 can only be <2>
R6C6 can only be <9>
R6C3 can only be <6>
R4C4 can only be <4>
R6C4 can only be <7>
R7C6 can only be <1>
R7C4 can only be <9>
R2C6 can only be <8>
R2C4 can only be <1>
R8C6 can only be <4>
R4C6 can only be <3>
R4C7 can only be <6>
R8C4 can only be <8>
R4C3 can only be <8>
R6C7 can only be <4>
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