The full reasoning can be found below the Sudoku.
Mar 09 - Very Hard
Puzzle Copyright © Kevin Stone
Reasoning
R9C8 can only be <5>
R3C3 is the only square in row 3 that can be <5>
R5C7 is the only square in row 5 that can be <5>
R4C5 is the only square in row 4 that can be <5>
R6C1 is the only square in row 6 that can be <3>
R8C1 is the only square in row 8 that can be <5>
R7C4 is the only square in row 7 that can be <5>
R7C5 is the only square in row 7 that can be <7>
R9C9 is the only square in row 9 that can be <3>
R9C4 is the only square in column 4 that can be <4>
R4C2 is the only square in column 2 that can be <4>
R9C2 is the only square in block 7 that can be <6>
R5C1 is the only square in row 5 that can be <6>
R4C1 is the only square in column 1 that can be <1>
R5C9 is the only square in row 5 that can be <1>
Intersection of row 5 with block 4. The value <9> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C3 - removing <9> from <289> leaving <28>
Squares R6C3 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <8> from <168> leaving <16>
R6C7 - removing <2> from <2469> leaving <469>
R6C9 - removing <28> from <2489> leaving <49>
R4C6 is the only square in block 5 that can be <8>
R4C7 is the only square in row 4 that can be <6>
R8C6 is the only square in column 6 that can be <6>
Intersection of column 5 with block 2. The value <9> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <9> from <1239> leaving <123>
R3C6 - removing <9> from <139> leaving <13>
Intersection of column 9 with block 3. The value <8> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <8> from <278> leaving <27>
Squares R2C7<29>, R6C7<49> and R7C7<24> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <249>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <29> from <1239> leaving <13>
R3C7 - removing <9> from <139> leaving <13>
Squares R3C6 and R3C7 in row 3 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.
R3C4 - removing <1> from <178> leaving <78>
R3C5 - removing <1> from <19> leaving <9>
Intersection of row 1 with block 1. The value <9> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <9> from <789> leaving <78>
Squares R3C6, R3C7, R1C6 and R1C7 form a Type-1 Unique Rectangle on <13>.
R1C6 - removing <13> from <123> leaving <2>
R1C8 can only be <7>
R7C6 can only be <9>
R2C5 can only be <6>
R5C8 can only be <8>
R3C9 can only be <8>
R6C5 can only be <1>
R3C4 can only be <7>
R5C2 can only be <9>
R6C8 can only be <2>
R6C4 can only be <6>
R8C5 can only be <2>
R6C3 can only be <8>
R4C9 can only be <7>
R7C1 can only be <8>
R9C6 can only be <1>
R8C9 can only be <4>
R8C3 can only be <1>
R6C9 can only be <9>
R7C7 can only be <2>
R9C3 can only be <9>
R3C6 can only be <3>
R2C4 can only be <8>
R3C7 can only be <1>
R1C7 can only be <3>
R4C3 can only be <2>
R5C3 can only be <7>
R1C2 can only be <8>
R7C3 can only be <4>
R6C7 can only be <4>
R2C9 can only be <2>
R1C1 can only be <9>
R2C1 can only be <7>
R2C7 can only be <9>
R1C4 can only be <1>
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