The full reasoning can be found below the Sudoku.
Apr 07 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C6 can only be <3>
R6C7 can only be <4>
R8C5 can only be <1>
R9C4 can only be <3>
R5C4 can only be <9>
R5C5 can only be <6>
R1C6 can only be <7>
R8C7 can only be <2>
R1C4 can only be <8>
R7C5 can only be <7>
R9C6 can only be <2>
R5C1 is the only square in row 5 that can be <7>
R9C8 is the only square in row 9 that can be <7>
R7C1 is the only square in column 1 that can be <2>
R3C1 is the only square in column 1 that can be <5>
R4C3 is the only square in column 3 that can be <2>
Squares R4C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <1> from <137> leaving <37>
R3C7 - removing <6> from <367> leaving <37>
Intersection of row 1 with block 1. The value <3> 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 <3> from <1349> leaving <149>
R2C3 - removing <3> from <1379> leaving <179>
R3C2 - removing <3> from <3489> leaving <489>
R3C3 - removing <3> from <3789> leaving <789>
R1C1 is the only square in column 1 that can be <3>
Intersection of column 8 with block 3. The value <4> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <4> from <124> leaving <12>
R2C9 - removing <4> from <149> leaving <19>
R3C9 - removing <4> from <469> leaving <69>
Intersection of column 9 with block 3. The value <9> 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.
R3C8 - removing <9> from <469> leaving <46>
Intersection of block 4 with column 2. The values <15> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain these values.
R1C2 - removing <1> from <14> leaving <4>
R7C2 - removing <1> from <1368> leaving <368>
R9C2 - removing <1> from <146> leaving <46>
R9C2 can only be <6>
R2C5 is the only square in row 2 that can be <4>
R3C5 can only be <3>
R3C7 can only be <7>
R2C7 can only be <3>
R2C3 is the only square in row 2 that can be <7>
R3C8 is the only square in row 3 that can be <4>
R3C9 is the only square in row 3 that can be <6>
R7C3 is the only square in column 3 that can be <1>
R7C7 can only be <6>
R9C1 can only be <4>
R7C8 can only be <5>
R4C7 can only be <1>
R7C9 can only be <8>
R6C8 can only be <9>
R7C2 can only be <3>
R8C9 can only be <4>
R8C1 can only be <9>
R9C9 can only be <1>
R1C9 can only be <2>
R2C9 can only be <9>
R1C8 can only be <1>
R5C9 can only be <5>
R2C1 can only be <1>
R4C2 can only be <9>
R5C8 can only be <2>
R5C2 can only be <1>
R6C3 can only be <3>
R4C8 can only be <6>
R6C2 can only be <5>
R8C3 can only be <8>
R3C3 can only be <9>
R3C2 can only be <8>
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