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The full reasoning can be found below the Sudoku.
Oct 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 can only be <6>
R3C7 can only be <8>
R2C8 can only be <5>
R1C8 can only be <3>
R1C4 is the only square in row 1 that can be <5>
R2C4 is the only square in row 2 that can be <1>
R8C1 is the only square in row 8 that can be <1>
R9C5 is the only square in row 9 that can be <1>
R2C1 is the only square in column 1 that can be <8>
R9C4 is the only square in column 4 that can be <8>
R1C6 is the only square in column 6 that can be <8>
R8C9 is the only square in column 9 that can be <7>
R8C2 is the only square in block 7 that can be <3>
R7C7 is the only square in block 9 that can be <4>
R6C7 can only be <5>
R5C3 is the only square in row 5 that can be <5>
R5C7 is the only square in row 5 that can be <1>
R4C7 can only be <6>
R4C1 can only be <4>
R4C9 can only be <9>
R6C1 can only be <3>
R6C9 can only be <4>
R5C1 can only be <6>
R5C9 can only be <3>
R4C3 is the only square in row 4 that can be <1>
Intersection of row 5 with block 5. The values <249> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R6C5 - removing <9> from <789> leaving <78>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C5 - removing <7> from <3679> leaving <369>
R7C5 - removing <7> from <367> leaving <36>
Squares R2C6<49>, R5C6<249>, R8C6<469> and R9C6<269> in column 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <69> from <3679> leaving <37>
R7C6 - removing <26> from <2367> leaving <37>
Intersection of column 6 with block 8. The value <6> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <6> from <36> leaving <3>
R7C6 can only be <7>
R7C4 can only be <2>
R3C6 can only be <3>
R7C3 can only be <6>
R3C3 can only be <9>
R9C2 can only be <2>
R4C2 can only be <7>
R3C4 can only be <7>
R3C5 can only be <6>
R6C3 can only be <2>
R2C2 can only be <4>
R1C5 can only be <4>
R4C5 can only be <8>
R6C2 can only be <9>
R4C8 can only be <2>
R6C5 can only be <7>
R6C8 can only be <8>
R1C2 can only be <6>
R5C5 can only be <9>
R2C6 can only be <9>
R9C6 can only be <6>
R5C4 can only be <4>
R9C8 can only be <9>
R8C6 can only be <4>
R8C8 can only be <6>
R5C6 can only be <2>
R8C4 can only be <9>
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