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The full reasoning can be found below the Sudoku.
Nov 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <8>
R3C6 is the only square in row 3 that can be <3>
R5C5 is the only square in row 5 that can be <8>
R9C2 is the only square in row 9 that can be <7>
R9C1 is the only square in row 9 that can be <8>
R7C6 is the only square in row 7 that can be <8>
R7C4 is the only square in row 7 that can be <2>
R8C7 is the only square in row 8 that can be <8>
R2C3 is the only square in column 3 that can be <7>
R2C4 is the only square in column 4 that can be <9>
R8C6 is the only square in column 6 that can be <7>
R3C4 is the only square in column 4 that can be <7>
R8C4 is the only square in column 4 that can be <5>
R2C5 is the only square in column 5 that can be <5>
R1C5 is the only square in column 5 that can be <2>
R2C6 can only be <1>
R4C7 is the only square in column 7 that can be <9>
Squares R1C1 and R1C2 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C8 - removing <1> from <179> leaving <79>
R1C9 - removing <1> from <179> leaving <79>
Squares R6C4 and R6C7 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <16> from <12456> leaving <245>
R6C3 - removing <1> from <134> leaving <34>
R6C8 - removing <16> from <13567> leaving <357>
R6C9 - removing <16> from <13567> leaving <357>
Squares R1C1 and R1C2 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C1 - removing <1> from <126> leaving <26>
Squares R5C8 and R6C7 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C9 - removing <16> from <1356> leaving <35>
Intersection of column 3 with block 4. The value <4> 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 this value.
R4C1 - removing <4> from <12456> leaving <1256>
R4C2 - removing <4> from <123456> leaving <12356>
R6C1 - removing <4> from <245> leaving <25>
Squares R2C2 and R2C8 in row 2 and R5C2 and R5C8 in row 5 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C8 - removing <6> from <1256> leaving <125>
R4C2 - removing <6> from <12356> leaving <1235>
R9C8 - removing <6> from <136> leaving <13>
R9C9 is the only square in row 9 that can be <6>
Squares R1C1, R1C2, R8C1 and R8C2 form a Type-4 Unique Rectangle on <14>.
R8C1 - removing <1> from <149> leaving <49>
R8C2 - removing <1> from <134> leaving <34>
Intersection of block 7 with row 7. The values <15> only appears in one or more of squares R7C1, R7C2 and R7C3 of block 7. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C9 - removing <1> from <139> leaving <39>
R3C9 is the only square in column 9 that can be <1>
R3C7 can only be <6>
R3C1 can only be <2>
R6C7 can only be <1>
R2C8 can only be <2>
R6C4 can only be <6>
R5C8 can only be <6>
R2C2 can only be <6>
R3C8 can only be <5>
R6C1 can only be <5>
R5C2 can only be <1>
R4C4 can only be <1>
R4C1 can only be <6>
R1C2 can only be <4>
R1C1 can only be <1>
R8C2 can only be <3>
R8C5 can only be <1>
R4C2 can only be <2>
R7C2 can only be <5>
R7C3 can only be <1>
R8C8 can only be <9>
R9C5 can only be <3>
R8C1 can only be <4>
R1C8 can only be <7>
R7C9 can only be <3>
R9C8 can only be <1>
R7C1 can only be <9>
R1C9 can only be <9>
R6C8 can only be <3>
R4C6 can only be <4>
R4C3 can only be <3>
R6C6 can only be <2>
R6C3 can only be <4>
R6C9 can only be <7>
R4C9 can only be <5>
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