The full reasoning can be found below the Sudoku.
Nov 04 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 can only be <6>
R6C3 can only be <5>
R4C7 can only be <8>
R6C6 can only be <2>
R4C3 can only be <6>
R1C8 is the only square in row 1 that can be <4>
R1C9 is the only square in row 1 that can be <2>
R5C9 can only be <9>
R5C8 can only be <2>
R9C9 can only be <3>
R9C1 can only be <5>
R1C2 is the only square in row 1 that can be <5>
R2C3 is the only square in row 2 that can be <2>
R2C7 is the only square in row 2 that can be <3>
Squares R5C1 and R5C2 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <37> from <378> leaving <8>
R5C5 - removing <7> from <1678> leaving <168>
R5C6 - removing <3> from <136> leaving <16>
Squares R7C2<149>, R7C3<189>, R8C3<18> and R9C2<149> in block 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1489>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C1 - removing <8> from <368> leaving <36>
R8C2 - removing <14> from <1346> leaving <36>
Intersection of column 1 with block 1. The value <8> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C3 - removing <8> from <189> leaving <19>
R3C8 is the only square in row 3 that can be <8>
R2C9 can only be <7>
R8C9 can only be <8>
R3C7 can only be <1>
R3C3 can only be <9>
R2C8 can only be <6>
R8C3 can only be <1>
R2C1 can only be <8>
R3C4 can only be <3>
R2C2 can only be <1>
R3C6 can only be <6>
R4C4 can only be <4>
R3C2 can only be <7>
R5C6 can only be <1>
R1C5 can only be <8>
R4C5 can only be <5>
R7C4 can only be <7>
R4C6 can only be <3>
R5C5 can only be <6>
R7C6 can only be <5>
R7C7 can only be <4>
R6C4 can only be <9>
R8C7 can only be <7>
R8C5 can only be <4>
R8C8 can only be <5>
R7C3 can only be <8>
R7C2 can only be <9>
R9C5 can only be <1>
R9C8 can only be <9>
R9C2 can only be <4>
R7C8 can only be <1>
R1C1 can only be <6>
R2C5 can only be <9>
R6C5 can only be <7>
R5C2 can only be <3>
R5C1 can only be <7>
R8C2 can only be <6>
R8C1 can only be <3>
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