The full reasoning can be found below the Sudoku.
Apr 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C2 can only be <4>
R8C2 can only be <5>
R7C2 can only be <9>
R2C3 is the only square in row 2 that can be <9>
R1C7 is the only square in row 1 that can be <9>
R3C6 is the only square in row 3 that can be <5>
R4C6 is the only square in row 4 that can be <7>
R4C1 is the only square in row 4 that can be <8>
R5C1 can only be <3>
R6C2 can only be <1>
R6C3 can only be <5>
R2C2 can only be <8>
R4C3 can only be <4>
R1C8 is the only square in row 1 that can be <4>
R3C1 is the only square in row 3 that can be <4>
R5C9 is the only square in row 5 that can be <6>
R5C6 is the only square in row 5 that can be <9>
R7C4 is the only square in row 7 that can be <5>
R7C9 is the only square in row 7 that can be <4>
R8C4 is the only square in row 8 that can be <4>
R3C3 is the only square in column 3 that can be <1>
R3C8 is the only square in row 3 that can be <6>
R6C9 is the only square in column 9 that can be <8>
R6C4 can only be <3>
R6C7 can only be <2>
Intersection of row 1 with block 2. The values <28> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R2C6 - removing <2> from <123> leaving <13>
Intersection of row 9 with block 8. The values <28> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C5 - removing <2> from <127> leaving <17>
R8C6 - removing <2> from <123> leaving <13>
R7C1 is the only square in row 7 that can be <2>
Squares R2C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C6 - removing <3> from <238> leaving <28>
Intersection of column 7 with block 9. The values <67> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C9 - removing <7> from <237> leaving <23>
Squares R8C6<13>, R8C8<123> and R8C9<23> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <123>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C7 - removing <13> from <1367> leaving <67>
Squares R1C6, R9C6, R1C5 and R9C5 form a Type-3 Unique Rectangle on <28>. Upon close inspection, it is clear that:
(R1C5 or R9C5)<37> and R3C5<37> form a naked pair on <37> in column 5. No other squares in the column can contain these possibilities
R7C5 - removing <7> from <17> leaving <1>
(R1C5 or R9C5)<37>, R7C5<17> and R3C5<37> form a naked triplet on <137> in column 5. No other squares in the column can contain these possibilities
R5C5 - removing <1> from <18> leaving <8>
R5C4 can only be <1>
R7C7 can only be <7>
R8C6 can only be <3>
R8C7 can only be <6>
R8C9 can only be <2>
R2C6 can only be <1>
R8C1 can only be <7>
R9C7 can only be <3>
R8C8 can only be <1>
R4C7 can only be <1>
R4C8 can only be <3>
R2C8 can only be <2>
R2C1 can only be <6>
R9C3 can only be <6>
R1C3 can only be <7>
R1C5 can only be <2>
R1C6 can only be <8>
R9C5 can only be <7>
R1C4 can only be <6>
R9C6 can only be <2>
R2C4 can only be <7>
R2C9 can only be <3>
R9C4 can only be <8>
R3C5 can only be <3>
R3C9 can only be <7>
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