The full reasoning can be found below the Sudoku.
Apr 18 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 can only be <8>
R7C6 can only be <1>
R2C2 can only be <1>
R2C9 can only be <2>
R2C3 can only be <9>
R2C5 can only be <4>
R1C2 is the only square in row 1 that can be <8>
R1C5 is the only square in row 1 that can be <9>
R4C5 is the only square in row 4 that can be <8>
R4C6 is the only square in row 4 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R5C9 is the only square in row 5 that can be <8>
R6C6 is the only square in row 6 that can be <4>
R7C8 is the only square in row 7 that can be <2>
R8C1 is the only square in row 8 that can be <1>
R7C7 is the only square in column 7 that can be <4>
R8C7 is the only square in column 7 that can be <6>
R1C9 is the only square in column 9 that can be <1>
Intersection of column 4 with block 5. The values <36> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R5C5 - removing <36> from <123567> leaving <1257>
R6C5 - removing <36> from <3567> leaving <57>
Squares R5C6 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C4 - removing <7> from <37> leaving <3>
R5C4 - removing <7> from <12367> leaving <1236>
R5C5 - removing <57> from <1257> leaving <12>
R6C4 - removing <7> from <367> leaving <36>
R4C1 can only be <5>
R6C4 can only be <6>
R4C7 can only be <7>
R3C2 is the only square in column 2 that can be <5>
Intersection of column 4 with block 2. The value <7> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <7> from <127> leaving <12>
Squares R5C4, R5C5, R3C4 and R3C5 form a Type-1 Unique Rectangle on <12>.
R3C4 - removing <12> from <127> leaving <7>
R3C8 can only be <3>
R1C4 can only be <2>
R3C3 can only be <2>
R1C7 can only be <5>
R1C1 can only be <3>
R5C4 can only be <1>
R3C5 can only be <1>
R1C8 can only be <7>
R5C7 can only be <3>
R5C5 can only be <2>
R5C1 can only be <4>
R6C9 can only be <5>
R6C5 can only be <7>
R9C9 can only be <3>
R5C2 can only be <6>
R9C1 can only be <2>
R5C3 can only be <7>
R7C2 can only be <3>
R9C2 can only be <4>
R5C6 can only be <5>
R6C3 can only be <3>
R9C6 can only be <7>
R8C3 can only be <8>
R7C5 can only be <6>
R9C5 can only be <5>
R8C8 can only be <5>
R9C3 can only be <6>
R8C5 can only be <3>
R9C8 can only be <8>
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