Oct 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C4 can only be <2>
R9C6 can only be <5>
R9C4 can only be <1>
R9C5 can only be <7>
R8C5 can only be <8>
R1C5 can only be <5>
R7C6 can only be <3>
R9C7 can only be <9>
R9C3 can only be <2>
R2C5 can only be <2>
R5C5 can only be <4>
R5C6 can only be <6>
R5C4 can only be <5>
R1C6 can only be <8>
R7C9 can only be <4>
R7C8 can only be <7>
R3C6 can only be <4>
R3C2 is the only square in row 3 that can be <7>
R3C1 is the only square in row 3 that can be <2>
R3C8 is the only square in row 3 that can be <8>
R4C7 is the only square in row 4 that can be <7>
R5C8 is the only square in row 5 that can be <1>
R8C8 can only be <3>
R8C9 can only be <1>
R4C1 is the only square in row 4 that can be <1>
R6C2 is the only square in row 6 that can be <2>
Squares R2C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C1 - removing <89> from <5689> leaving <56>
Intersection of row 5 with block 4. The value <9> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. 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 <9> from <489> leaving <48>
Intersection of column 3 with block 4. The values <48> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C2 - removing <8> from <389> leaving <39>
Squares R2C2<389>, R5C2<39> and R7C2<89> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <389>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <3> from <356> leaving <56>
Squares R7C1, R7C2, R2C1 and R2C2 form a Type-1 Unique Rectangle on <89>.
R2C2 - removing <89> from <389> leaving <3>
R5C2 can only be <9>
R1C3 can only be <9>
R7C2 can only be <8>
R7C1 can only be <9>
R1C4 can only be <6>
R2C1 can only be <8>
R1C7 can only be <3>
R3C4 can only be <9>
R5C7 can only be <8>
R3C9 can only be <6>
R5C3 can only be <3>
R6C7 can only be <6>
R6C1 can only be <5>
R4C3 can only be <4>
R6C9 can only be <9>
R8C1 can only be <6>
R4C2 can only be <6>
R6C8 can only be <4>
R2C9 can only be <5>
R8C2 can only be <5>
R2C8 can only be <9>
R4C9 can only be <3>
R4C8 can only be <5>
R6C3 can only be <8>
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