The full reasoning can be found below the Sudoku.
Mar 05 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R4C3 can only be <3>
R4C4 can only be <6>
R6C6 can only be <4>
R4C6 can only be <9>
R6C4 can only be <7>
R4C7 can only be <5>
R2C4 can only be <5>
R6C3 can only be <1>
R5C6 can only be <3>
R2C6 can only be <1>
R8C4 can only be <2>
R8C6 can only be <5>
R6C7 can only be <6>
R5C3 can only be <4>
R5C4 can only be <8>
R9C5 can only be <4>
R8C5 can only be <3>
R5C2 can only be <6>
R5C5 can only be <2>
R7C5 can only be <6>
R2C8 is the only square in row 2 that can be <6>
R3C2 is the only square in row 3 that can be <3>
R3C3 is the only square in row 3 that can be <5>
R7C8 is the only square in row 7 that can be <3>
R7C2 is the only square in row 7 that can be <5>
R9C2 can only be <8>
R7C3 is the only square in row 7 that can be <7>
R1C3 can only be <9>
R9C3 can only be <2>
R9C7 can only be <9>
R9C8 can only be <5>
R5C7 can only be <1>
R5C8 can only be <9>
R8C9 is the only square in row 8 that can be <8>
R8C1 is the only square in row 8 that can be <9>
Intersection of row 2 with block 1. The value <4> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <4> from <147> leaving <17>
Squares R1C2 and R1C8 in row 1 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C8 - removing <1> from <17> leaving <7>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R3C9=<19>
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
R3C9 - removing <19> from <129> leaving <2>
R3C1 can only be <1>
R3C7 can only be <8>
R2C9 can only be <9>
R7C9 can only be <1>
R7C1 can only be <4>
R8C8 can only be <4>
R8C2 can only be <1>
R1C8 can only be <1>
R7C7 can only be <2>
R1C2 can only be <7>
R2C5 can only be <7>
R3C5 can only be <9>
R1C7 can only be <4>
R2C1 can only be <2>
R1C5 can only be <8>
R2C2 can only be <4>
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