The full reasoning can be found below the Sudoku.
Apr 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <4>
R9C7 can only be <6>
R8C5 can only be <6>
R1C4 is the only square in row 1 that can be <3>
R1C6 is the only square in row 1 that can be <5>
R2C8 is the only square in row 2 that can be <9>
R8C8 can only be <4>
R8C2 can only be <7>
R7C9 can only be <9>
R9C9 can only be <5>
R8C4 can only be <5>
R8C6 can only be <9>
R1C1 is the only square in row 1 that can be <9>
R1C3 is the only square in row 1 that can be <4>
R9C3 can only be <2>
R9C5 can only be <8>
R6C3 can only be <8>
R7C1 can only be <4>
R6C7 can only be <9>
R4C3 can only be <5>
R7C4 can only be <2>
R7C6 can only be <1>
R9C1 can only be <3>
R2C4 can only be <7>
R3C6 can only be <4>
R2C6 can only be <8>
R9C4 can only be <4>
R3C4 can only be <6>
R9C6 can only be <7>
Squares R3C1 and R4C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C1 - removing <1> from <167> leaving <67>
R6C1 - removing <2> from <267> leaving <67>
Intersection of column 8 with block 6. The values <236> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C9 - removing <2> from <1248> leaving <148>
R6C9 - removing <2> from <247> leaving <47>
Squares R1C7, R4C7, R1C9 and R4C9 form a Type-4 Unique Rectangle on <18>.
R1C9 - removing <1> from <128> leaving <28>
R4C9 - removing <1> from <148> leaving <48>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R4C2=<34>
These are called the BUG possibilities. In a BUG pattern, in each row, column and block, each unsolved possibility appears exactly twice. Such a pattern either has 0 or 2 solutions, so it cannot be part of a valid Sudoku
When a puzzle contains a BUG, and only one square in the puzzle has more than 2 possibilities, the only way to kill the BUG is to remove both of the BUG possibilities from the square, thus solving it
R4C2 - removing <34> from <1234> leaving <12>
R4C8 is the only square in row 4 that can be <3>
R5C8 can only be <6>
R5C1 can only be <7>
R6C8 can only be <2>
R6C2 can only be <4>
R5C9 can only be <1>
R6C1 can only be <6>
R5C2 can only be <3>
R3C9 can only be <2>
R4C7 can only be <8>
R6C9 can only be <7>
R3C1 can only be <1>
R1C9 can only be <8>
R4C9 can only be <4>
R1C7 can only be <1>
R1C5 can only be <2>
R4C1 can only be <2>
R2C2 can only be <2>
R4C2 can only be <1>
R2C5 can only be <1>
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