The full reasoning can be found below the Sudoku.
Jun 09 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <4>
R9C9 can only be <6>
R9C8 can only be <8>
R7C8 can only be <1>
R3C8 can only be <5>
R5C8 can only be <6>
R3C6 is the only square in row 3 that can be <1>
R2C9 is the only square in row 2 that can be <1>
R4C5 is the only square in row 4 that can be <6>
R6C5 is the only square in row 6 that can be <1>
R6C4 is the only square in row 6 that can be <3>
Squares R2C3 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <9> from <379> leaving <37>
R2C7 - removing <9> from <379> leaving <37>
Intersection of row 4 with block 5. The value <7> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <7> from <2789> leaving <289>
R5C6 - removing <7> from <4579> leaving <459>
Intersection of row 8 with block 9. The value <7> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <7> from <247> leaving <24>
Intersection of column 4 with block 5. The value <8> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <8> from <2489> leaving <249>
Squares R3C2<36>, R7C2<46> and R9C2<34> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <346>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C2 - removing <4> from <478> leaving <78>
R4C3 is the only square in block 4 that can be <4>
R4C6 can only be <7>
R7C4 is the only square in row 7 that can be <7>
Squares R3C3 and R3C4 in row 3, R4C4 and R4C7 in row 4 and R7C3 and R7C7 in row 7 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 3, 4 and 7 can be removed.
R5C4 - removing <2> from <289> leaving <89>
R8C3 - removing <2> from <25> leaving <5>
R8C7 - removing <2> from <247> leaving <47>
R6C3 can only be <8>
R6C7 can only be <9>
R2C3 can only be <9>
R5C2 can only be <7>
R6C6 can only be <5>
R3C7 can only be <3>
R5C9 can only be <2>
R2C5 can only be <8>
R3C2 can only be <6>
R2C7 can only be <7>
R5C1 can only be <5>
R1C2 can only be <8>
R8C9 can only be <7>
R4C7 can only be <8>
R8C7 can only be <4>
R1C9 can only be <9>
R1C5 can only be <2>
R2C1 can only be <3>
R3C3 can only be <2>
R7C2 can only be <4>
R3C4 can only be <9>
R7C3 can only be <6>
R1C1 can only be <7>
R5C4 can only be <8>
R4C4 can only be <2>
R7C6 can only be <9>
R7C7 can only be <2>
R9C2 can only be <3>
R5C6 can only be <4>
R8C5 can only be <3>
R9C1 can only be <9>
R9C5 can only be <4>
R8C1 can only be <2>
R5C5 can only be <9>
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