The full reasoning can be found below the Sudoku.
Apr 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C1 can only be <8>
R2C3 is the only square in row 2 that can be <4>
R8C3 can only be <2>
R8C1 can only be <1>
R5C3 can only be <7>
R7C3 can only be <6>
R3C3 can only be <8>
R2C1 is the only square in row 2 that can be <7>
R3C8 is the only square in row 3 that can be <7>
R5C5 is the only square in row 5 that can be <1>
R6C2 is the only square in row 6 that can be <1>
R6C5 is the only square in row 6 that can be <7>
R9C9 is the only square in row 9 that can be <6>
R1C2 is the only square in row 1 that can be <6>
R3C7 is the only square in row 3 that can be <6>
R9C5 is the only square in column 5 that can be <3>
R8C7 is the only square in row 8 that can be <3>
R5C4 is the only square in row 5 that can be <3>
R6C8 is the only square in row 6 that can be <3>
Squares R6C4 and R6C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C4 - removing <9> from <589> leaving <58>
R4C5 - removing <9> from <2489> leaving <248>
R4C6 - removing <9> from <2459> leaving <245>
R5C6 - removing <9> from <2459> leaving <245>
Intersection of block 8 with row 8. The value <5> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C9 - removing <5> from <459> leaving <49>
Squares R5C6 and R5C9 in row 5 and R8C6 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 6 and 9 can be removed.
R4C6 - removing <4> from <245> leaving <25>
Squares R6C4, R6C6, R2C4 and R2C6 form a Type-4 Unique Rectangle on <69>.
R2C4 - removing <9> from <689> leaving <68>
R2C6 - removing <9> from <269> leaving <26>
Intersection of row 2 with block 3. The value <9> 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.
R1C8 - removing <9> from <259> leaving <25>
R1C9 - removing <9> from <589> leaving <58>
Intersection of block 2 with column 5. The value <9> only appears in one or more of squares R1C5, R2C5 and R3C5 of block 2. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R7C5 - removing <9> from <49> leaving <4>
R7C2 can only be <5>
R9C2 can only be <4>
R9C8 can only be <5>
R1C8 can only be <2>
R1C1 can only be <9>
R7C8 can only be <9>
R2C7 can only be <9>
R2C9 can only be <8>
R5C7 can only be <5>
R7C7 can only be <2>
R2C4 can only be <6>
R1C9 can only be <5>
R4C8 can only be <4>
R8C9 can only be <4>
R5C9 can only be <9>
R1C5 can only be <8>
R5C1 can only be <2>
R3C2 can only be <2>
R4C5 can only be <2>
R2C6 can only be <2>
R6C4 can only be <9>
R4C6 can only be <5>
R5C6 can only be <4>
R3C5 can only be <9>
R4C2 can only be <9>
R4C4 can only be <8>
R8C6 can only be <9>
R6C6 can only be <6>
R8C4 can only be <5>
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