Jan 29 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <7>
R2C7 is the only square in row 2 that can be <6>
R3C8 is the only square in row 3 that can be <1>
R2C8 can only be <3>
R2C2 can only be <5>
R3C2 can only be <3>
R7C2 can only be <2>
R3C4 can only be <5>
R3C6 can only be <4>
R7C4 can only be <6>
R7C8 can only be <4>
R5C2 can only be <4>
R8C2 can only be <7>
R7C6 can only be <5>
R5C1 is the only square in row 5 that can be <3>
R4C7 is the only square in row 4 that can be <3>
R6C9 is the only square in row 6 that can be <6>
R5C6 is the only square in row 5 that can be <6>
R6C5 is the only square in row 6 that can be <4>
R4C9 is the only square in row 4 that can be <4>
R6C3 is the only square in row 6 that can be <9>
Intersection of row 9 with block 8. The values <23> 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.
R8C5 - removing <2> from <289> leaving <89>
Squares R2C3 and R2C5 in row 2 and R8C3 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 5 can be removed.
R1C5 - removing <8> from <1238> leaving <123>
R5C5 - removing <8> from <258> leaving <25>
R9C5 - removing <8> from <2389> leaving <239>
R5C4 is the only square in row 5 that can be <8>
Squares R4C5 and R5C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <2> from <123> leaving <13>
R9C5 - removing <2> from <239> leaving <39>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R4C1=<12>
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
R4C1 - removing <12> from <125> leaving <5>
R4C3 can only be <1>
R4C5 can only be <2>
R6C1 can only be <2>
R9C1 can only be <8>
R2C3 can only be <8>
R5C5 can only be <5>
R5C9 can only be <9>
R5C8 can only be <2>
R9C9 can only be <5>
R6C7 can only be <5>
R8C7 can only be <2>
R8C8 can only be <9>
R8C5 can only be <8>
R9C6 can only be <2>
R1C1 can only be <1>
R8C3 can only be <5>
R9C4 can only be <3>
R1C6 can only be <8>
R1C5 can only be <3>
R1C4 can only be <2>
R9C5 can only be <9>
R2C5 can only be <1>
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