The full reasoning can be found below the Sudoku.
Apr 15 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 can only be <6>
R9C8 can only be <2>
R9C5 is the only square in row 9 that can be <8>
Squares R1C3, R2C1 and R3C1 in block 1 form a simple naked triplet. These 3 squares all contain the 3 possibilities <248>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C3 - removing <248> from <23489> leaving <39>
Intersection of row 6 with block 5. The value <5> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. 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 <5> from <12345679> leaving <1234679>
R5C6 - removing <5> from <15789> leaving <1789>
Intersection of block 2 with row 3. The value <8> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <8> from <248> leaving <24>
R3C9 - removing <8> from <23478> leaving <2347>
Intersection of block 6 with row 5. The value <8> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C1 - removing <8> from <568> leaving <56>
R5C3 - removing <8> from <3678> leaving <367>
R5C4 - removing <8> from <23468> leaving <2346>
R5C6 - removing <8> from <1789> leaving <179>
R2C1 is the only square in column 1 that can be <8>
R1C8 is the only square in row 1 that can be <8>
R5C9 is the only square in row 5 that can be <8>
R8C8 is the only square in column 8 that can be <5>
R8C2 can only be <7>
R9C2 can only be <9>
R9C3 can only be <6>
R2C2 can only be <3>
R9C7 can only be <7>
R8C1 can only be <4>
R2C8 can only be <4>
R5C2 can only be <5>
R3C3 can only be <9>
R2C9 can only be <2>
R5C8 can only be <3>
R2C5 can only be <9>
R1C7 can only be <5>
R5C1 can only be <6>
R5C3 can only be <7>
R6C7 can only be <4>
R8C9 can only be <3>
R3C1 can only be <2>
R7C3 can only be <2>
R8C5 can only be <6>
R3C9 can only be <7>
R7C9 can only be <4>
R7C7 can only be <6>
R3C7 can only be <3>
R7C1 can only be <5>
R1C3 can only be <4>
R7C4 can only be <3>
R1C5 can only be <2>
R4C5 can only be <3>
R4C3 can only be <8>
R6C4 can only be <8>
R6C3 can only be <3>
R3C4 can only be <4>
R4C6 can only be <9>
R3C5 can only be <5>
R5C4 can only be <2>
R3C6 can only be <8>
R6C5 can only be <7>
R4C7 can only be <2>
R5C6 can only be <1>
R4C4 can only be <6>
R5C7 can only be <9>
R5C5 can only be <4>
R7C6 can only be <7>
R6C6 can only be <5>
R7C5 can only be <1>
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