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The full reasoning can be found below the Sudoku.
Nov 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C5 can only be <3>
R8C4 can only be <9>
R2C5 can only be <5>
R8C6 can only be <4>
R8C9 can only be <2>
R8C7 can only be <5>
R8C1 can only be <8>
R6C7 can only be <6>
R5C7 can only be <2>
R7C7 can only be <7>
R3C7 can only be <3>
R1C9 can only be <9>
R2C9 can only be <6>
R6C9 can only be <1>
R6C6 can only be <3>
R5C9 can only be <4>
R9C9 can only be <3>
R6C4 can only be <5>
R6C8 can only be <9>
R5C8 can only be <5>
R9C6 is the only square in row 9 that can be <7>
R5C4 is the only square in row 5 that can be <7>
R4C3 is the only square in column 3 that can be <5>
Squares R3C2 and R3C3 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C6 - removing <19> from <1289> leaving <28>
R2C6 is the only square in column 6 that can be <9>
R5C1 is the only square in column 1 that can be <9>
Squares R3C2 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <1> from <125> leaving <25>
R1C2 - removing <1> from <135> leaving <35>
Intersection of column 6 with block 5. The value <1> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <1> from <126> leaving <26>
R5C5 - removing <1> from <168> leaving <68>
Squares R3C2, R3C3, R7C2 and R7C3 form a Type-2 Unique Rectangle on <19>.
R9C1 - removing <4> from <145> leaving <15>
R9C2 - removing <4> from <145> leaving <15>
R7C8 - removing <4> from <46> leaving <6>
R7C4 can only be <1>
R9C8 can only be <4>
R9C5 can only be <6>
R5C5 can only be <8>
R5C6 can only be <1>
R1C5 can only be <1>
R5C3 can only be <3>
R4C6 can only be <2>
R4C4 can only be <6>
R3C6 can only be <8>
R5C2 can only be <6>
R2C3 can only be <4>
R2C1 can only be <2>
R7C3 can only be <9>
R3C8 can only be <2>
R1C8 can only be <8>
R7C2 can only be <4>
R3C3 can only be <1>
R2C4 can only be <3>
R1C1 can only be <5>
R1C4 can only be <2>
R3C2 can only be <9>
R4C2 can only be <1>
R1C2 can only be <3>
R9C1 can only be <1>
R4C1 can only be <4>
R9C2 can only be <5>
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