The full reasoning can be found below the Sudoku.
Apr 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C8 is the only square in row 5 that can be <7>
R2C7 is the only square in row 2 that can be <7>
R4C3 is the only square in row 4 that can be <7>
R6C3 is the only square in row 6 that can be <2>
R7C5 is the only square in row 7 that can be <7>
R3C1 is the only square in column 1 that can be <2>
R2C4 is the only square in column 4 that can be <5>
R8C6 is the only square in column 6 that can be <4>
R1C6 is the only square in column 6 that can be <2>
Squares R5C4, R5C5 and R5C6 in row 5 form a simple naked triplet. These 3 squares all contain the 3 possibilities <136>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C1 - removing <6> from <4568> leaving <458>
R5C2 - removing <36> from <34568> leaving <458>
R5C9 - removing <36> from <3568> leaving <58>
R6C9 is the only square in column 9 that can be <6>
Intersection of row 5 with block 4. The value <4> 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.
R6C2 - removing <4> from <348> leaving <38>
Intersection of column 1 with block 4. The value <5> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <5> from <356> leaving <36>
R5C2 - removing <5> from <458> leaving <48>
Intersection of column 3 with block 7. The values <46> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <46> from <468> leaving <8>
R8C2 - removing <6> from <5689> leaving <589>
R9C2 - removing <4> from <1489> leaving <189>
R7C9 can only be <3>
R7C7 can only be <4>
R6C8 is the only square in row 6 that can be <4>
R9C3 is the only square in row 9 that can be <4>
Intersection of column 4 with block 8. The value <8> only appears in one or more of squares R7C4, R8C4 and R9C4 of column 4. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C5 - removing <8> from <2368> leaving <236>
R9C5 - removing <8> from <128> leaving <12>
Squares R1C5<136>, R2C6<16> and R3C6<13> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <136>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C5 - removing <16> from <1689> leaving <89>
R3C5 - removing <13> from <1389> leaving <89>
Squares R2C1<46>, R2C2<146> and R2C6<16> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <146>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C8 - removing <1> from <189> leaving <89>
R1C8 is the only square in column 8 that can be <1>
R4C8 is the only square in column 8 that can be <3>
R4C2 can only be <6>
R6C7 can only be <8>
R6C2 can only be <3>
R5C9 can only be <5>
R4C1 can only be <5>
R1C2 can only be <5>
R5C1 can only be <4>
R4C7 can only be <9>
R1C7 can only be <3>
R8C2 can only be <9>
R3C3 can only be <1>
R1C5 can only be <6>
R3C6 can only be <3>
R7C3 can only be <6>
R2C2 can only be <4>
R3C7 can only be <5>
R5C2 can only be <8>
R2C1 can only be <6>
R7C4 can only be <1>
R8C3 can only be <5>
R9C4 can only be <8>
R9C5 can only be <2>
R8C9 can only be <8>
R9C2 can only be <1>
R8C8 can only be <2>
R3C9 can only be <9>
R9C8 can only be <9>
R2C8 can only be <8>
R8C5 can only be <3>
R2C6 can only be <1>
R5C6 can only be <6>
R2C5 can only be <9>
R3C5 can only be <8>
R5C4 can only be <3>
R8C4 can only be <6>
R5C5 can only be <1>
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