The full reasoning can be found below the Sudoku.
Apr 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 can only be <9>
R6C4 can only be <4>
R6C5 can only be <5>
R6C3 can only be <9>
R4C5 can only be <6>
R4C3 can only be <5>
R6C8 can only be <1>
R5C2 can only be <6>
R6C7 can only be <3>
R4C7 can only be <7>
R4C2 can only be <1>
R5C3 can only be <2>
R1C3 can only be <4>
R1C4 is the only square in row 1 that can be <3>
R1C7 is the only square in row 1 that can be <1>
R9C3 is the only square in row 9 that can be <6>
R7C4 is the only square in row 7 that can be <6>
R9C9 is the only square in row 9 that can be <3>
R9C6 is the only square in row 9 that can be <1>
R8C4 can only be <9>
R3C4 can only be <1>
R8C2 is the only square in column 2 that can be <4>
R7C6 is the only square in column 6 that can be <7>
Squares R7C3 and R7C5 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <8> from <158> leaving <15>
R7C7 - removing <8> from <4589> leaving <459>
R7C8 - removing <8> from <589> leaving <59>
Squares R7C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <8> from <289> leaving <29>
R3C5 - removing <8> from <289> leaving <29>
Intersection of row 2 with block 3. The value <7> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C9 - removing <7> from <479> leaving <49>
Squares R7C3, R7C5, R8C3 and R8C5 form a Type-1 Unique Rectangle on <38>.
R8C3 - removing <38> from <378> leaving <7>
R8C9 can only be <1>
R3C3 can only be <8>
R9C2 can only be <5>
R8C1 can only be <8>
R9C7 can only be <8>
R1C2 can only be <9>
R7C1 can only be <1>
R9C8 can only be <7>
R5C7 can only be <9>
R3C2 can only be <7>
R3C6 can only be <4>
R7C3 can only be <3>
R3C9 can only be <9>
R2C6 can only be <8>
R3C5 can only be <2>
R7C9 can only be <4>
R2C8 can only be <2>
R5C8 can only be <8>
R7C5 can only be <8>
R8C5 can only be <3>
R7C7 can only be <5>
R2C9 can only be <7>
R2C1 can only be <6>
R2C5 can only be <9>
R1C8 can only be <5>
R7C8 can only be <9>
R3C7 can only be <6>
R1C1 can only be <2>
R2C7 can only be <4>
R3C1 can only be <5>
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