Feb 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <6>
R9C1 can only be <3>
R1C5 can only be <8>
R3C1 can only be <8>
R1C1 can only be <2>
R2C4 can only be <4>
R3C5 can only be <1>
R7C1 can only be <5>
R5C1 can only be <7>
R5C3 can only be <1>
R1C9 is the only square in row 1 that can be <5>
R3C2 is the only square in row 3 that can be <3>
R4C6 is the only square in row 4 that can be <5>
R4C5 is the only square in row 4 that can be <7>
R5C6 is the only square in row 5 that can be <3>
R7C8 is the only square in row 7 that can be <3>
R7C2 is the only square in row 7 that can be <8>
R8C8 is the only square in row 8 that can be <5>
R8C2 is the only square in column 2 that can be <6>
R8C4 can only be <1>
R9C3 can only be <4>
R8C6 can only be <2>
R8C7 can only be <4>
R6C6 can only be <1>
R8C3 can only be <7>
R2C3 can only be <9>
R2C2 can only be <7>
R1C3 can only be <6>
R1C7 can only be <9>
Squares R7C5 and R9C5 in column 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 column.
R5C5 - removing <6> from <246> leaving <24>
R6C5 - removing <9> from <249> leaving <24>
Squares R7C5, R7C9, R9C5 and R9C9 form a Type-1 Unique Rectangle on <69>.
R9C9 - removing <69> from <269> leaving <2>
R9C7 can only be <6>
R9C5 can only be <9>
R7C9 can only be <9>
R7C5 can only be <6>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R6C8=<48>
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
R6C8 - removing <48> from <248> leaving <2>
R6C2 can only be <9>
R6C5 can only be <4>
R2C8 can only be <8>
R4C8 can only be <6>
R5C7 can only be <8>
R2C7 can only be <2>
R4C4 can only be <9>
R3C8 can only be <4>
R5C9 can only be <4>
R5C4 can only be <6>
R5C5 can only be <2>
R3C9 can only be <6>
R6C4 can only be <8>
R4C2 can only be <2>
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