The full reasoning can be found below the Sudoku.
Apr 15 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <6>
R6C7 can only be <6>
R1C7 can only be <3>
R6C5 can only be <8>
R3C2 is the only square in row 3 that can be <3>
R4C5 is the only square in row 4 that can be <1>
R7C5 can only be <7>
R3C5 can only be <6>
R3C4 is the only square in row 3 that can be <7>
R5C8 is the only square in row 5 that can be <7>
R5C2 is the only square in row 5 that can be <8>
R7C3 is the only square in row 7 that can be <5>
R7C9 is the only square in row 7 that can be <6>
R8C1 is the only square in row 8 that can be <7>
R9C7 is the only square in row 9 that can be <7>
R9C2 is the only square in row 9 that can be <1>
R9C3 is the only square in column 3 that can be <8>
R9C4 can only be <4>
R1C3 is the only square in column 3 that can be <9>
R1C6 can only be <4>
Squares R7C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <4> from <246> leaving <26>
Intersection of block 4 with row 4. The value <2> only appears in one or more of squares R4C1, R4C2 and R4C3 of block 4. These squares are the ones that intersect with row 4. Thus, the other (non-intersecting) squares of row 4 cannot contain this value.
R4C4 - removing <2> from <236> leaving <36>
R4C9 - removing <2> from <234> leaving <34>
Squares R7C4<28>, R7C6<128> and R7C7<18> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <128>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C8 - removing <1> from <149> leaving <49>
Squares R7C2, R7C8, R8C2 and R8C8 form a Type-1 Unique Rectangle on <49>.
R8C8 - removing <49> from <149> leaving <1>
R7C7 can only be <8>
R7C4 can only be <2>
R3C7 can only be <1>
R8C9 can only be <4>
R8C2 can only be <9>
R4C9 can only be <3>
R7C8 can only be <9>
R3C1 can only be <4>
R4C4 can only be <6>
R5C9 can only be <2>
R2C9 can only be <8>
R6C8 can only be <4>
R6C1 can only be <9>
R7C6 can only be <1>
R7C2 can only be <4>
R2C4 can only be <9>
R3C3 can only be <2>
R3C8 can only be <5>
R4C3 can only be <4>
R2C2 can only be <6>
R3C6 can only be <8>
R2C8 can only be <2>
R4C2 can only be <2>
R6C6 can only be <2>
R5C1 can only be <6>
R2C1 can only be <1>
R2C6 can only be <5>
R5C4 can only be <3>
R8C6 can only be <3>
R5C6 can only be <9>
R8C4 can only be <8>
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