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The full reasoning can be found below the Sudoku.
Nov 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <7>
R3C1 is the only square in row 3 that can be <4>
R3C5 is the only square in row 3 that can be <8>
R1C8 is the only square in row 1 that can be <8>
R4C5 is the only square in row 4 that can be <6>
R5C6 is the only square in row 5 that can be <7>
R5C4 is the only square in row 5 that can be <8>
R6C1 is the only square in row 6 that can be <8>
R7C9 is the only square in row 7 that can be <7>
R8C8 is the only square in row 8 that can be <6>
R5C7 is the only square in row 5 that can be <6>
R9C2 is the only square in row 9 that can be <7>
R9C3 is the only square in row 9 that can be <9>
R1C2 is the only square in row 1 that can be <9>
R4C1 is the only square in column 1 that can be <9>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <13> from <1235> leaving <25>
R1C7 - removing <13> from <1235> leaving <25>
Squares R5C2 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <2> from <259> leaving <59>
Squares R1C4 and R4C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C4 - removing <1> from <124> leaving <24>
R9C4 - removing <1> from <124> leaving <24>
Intersection of column 1 with block 7. The value <2> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <2> from <1235> leaving <135>
R8C2 - removing <2> from <123> leaving <13>
R5C2 is the only square in column 2 that can be <2>
R5C3 can only be <3>
Intersection of row 3 with block 3. The value <3> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <3> from <1359> leaving <159>
Intersection of block 6 with column 9. The value <1> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R2C9 - removing <1> from <159> leaving <59>
R3C9 - removing <1> from <123> leaving <23>
R8C9 - removing <1> from <1235> leaving <235>
Squares R2C9<59>, R4C9<15> and R6C9<19> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <159>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C9 - removing <5> from <235> leaving <23>
Squares R1C4, R1C6, R4C4 and R4C6 form a Type-1 Unique Rectangle on <13>.
R4C6 - removing <13> from <135> leaving <5>
R4C9 can only be <1>
R5C5 can only be <9>
R4C4 can only be <3>
R6C9 can only be <9>
R5C8 can only be <5>
R9C8 can only be <1>
R2C9 can only be <5>
R9C6 can only be <4>
R2C8 can only be <9>
R2C1 can only be <3>
R1C7 can only be <2>
R1C4 can only be <1>
R9C4 can only be <2>
R6C6 can only be <1>
R1C6 can only be <3>
R1C3 can only be <5>
R9C7 can only be <5>
R3C9 can only be <3>
R2C2 can only be <1>
R8C2 can only be <3>
R3C3 can only be <2>
R3C7 can only be <1>
R8C9 can only be <2>
R6C5 can only be <2>
R8C1 can only be <5>
R6C4 can only be <4>
R7C7 can only be <3>
R7C3 can only be <1>
R7C5 can only be <5>
R7C1 can only be <2>
R8C5 can only be <1>
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