The full reasoning can be found below the Sudoku.
Mar 07 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R8C5 can only be <7>
R8C4 can only be <2>
R6C5 is the only square in row 6 that can be <5>
R9C6 is the only square in row 9 that can be <4>
R2C6 can only be <7>
R6C4 is the only square in row 6 that can be <4>
R4C4 is the only square in column 4 that can be <7>
R5C4 is the only square in column 4 that can be <9>
R2C1 is the only square in column 1 that can be <9>
R3C5 is the only square in block 2 that can be <3>
R2C5 is the only square in column 5 that can be <4>
Squares R7C5 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C7 - removing <68> from <12689> leaving <129>
R7C8 - removing <8> from <1258> leaving <125>
R7C9 - removing <6> from <2569> leaving <259>
Intersection of row 5 with block 5. The value <8> 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 this value.
R4C5 - removing <8> from <168> leaving <16>
R4C6 - removing <8> from <2368> leaving <236>
R6C6 - removing <8> from <368> leaving <36>
Intersection of column 2 with block 4. The value <9> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C3 - removing <9> from <1689> leaving <168>
R6C3 - removing <9> from <6789> leaving <678>
Intersection of column 9 with block 9. The value <9> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. 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 <9> from <129> leaving <12>
R8C7 - removing <9> from <39> leaving <3>
Squares R2C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <1> from <147> leaving <47>
R3C7 - removing <12> from <1247> leaving <47>
R4C7 - removing <2> from <2689> leaving <689>
R9C7 - removing <12> from <12678> leaving <678>
R2C7 is the only square in block 3 that can be <2>
R2C3 can only be <1>
R7C7 can only be <1>
R3C4 is the only square in row 3 that can be <1>
R1C4 can only be <6>
R1C8 is the only square in row 1 that can be <1>
R1C9 is the only square in row 1 that can be <5>
R8C9 can only be <9>
R8C3 can only be <5>
R7C9 can only be <2>
R7C8 can only be <5>
R5C9 can only be <6>
R9C8 can only be <8>
R7C3 can only be <9>
R6C8 can only be <3>
R5C1 can only be <1>
R9C9 can only be <7>
R6C6 can only be <6>
R4C8 can only be <2>
R9C7 can only be <6>
R5C5 can only be <8>
R9C1 can only be <3>
R5C6 can only be <2>
R7C5 can only be <6>
R4C6 can only be <3>
R7C6 can only be <8>
R4C5 can only be <1>
R9C3 can only be <2>
R1C1 can only be <4>
R9C2 can only be <1>
R1C7 can only be <7>
R3C1 can only be <6>
R1C2 can only be <8>
R3C7 can only be <4>
R3C3 can only be <7>
R3C2 can only be <2>
R6C3 can only be <8>
R6C7 can only be <9>
R1C3 can only be <3>
R4C3 can only be <6>
R4C2 can only be <9>
R6C2 can only be <7>
R4C7 can only be <8>
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