Feb 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <7>
R2C7 can only be <3>
R7C2 can only be <6>
R7C8 can only be <9>
R2C5 can only be <5>
R8C3 can only be <1>
R3C2 can only be <5>
R2C9 can only be <6>
R8C7 can only be <4>
R2C4 can only be <9>
R3C8 can only be <7>
R1C1 can only be <8>
R1C2 can only be <3>
R2C1 can only be <4>
R2C6 can only be <8>
R4C6 is the only square in row 4 that can be <1>
R6C1 is the only square in row 6 that can be <6>
R6C2 is the only square in row 6 that can be <2>
R6C6 is the only square in row 6 that can be <9>
R8C6 is the only square in row 8 that can be <5>
R8C9 is the only square in row 8 that can be <8>
R4C8 is the only square in row 4 that can be <8>
R9C2 is the only square in row 9 that can be <8>
R4C1 is the only square in column 1 that can be <5>
Squares R9C8 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <3> from <2367> leaving <267>
Squares R1C4, R1C6, R9C4 and R9C6 form a Type-1 Unique Rectangle on <67>.
R9C4 - removing <67> from <267> leaving <2>
R9C1 can only be <7>
R9C6 can only be <6>
R8C1 can only be <2>
R1C6 can only be <7>
R1C4 can only be <6>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R4C4=<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
R4C4 - removing <34> from <347> leaving <7>
R4C2 can only be <4>
R4C9 can only be <3>
R6C4 can only be <4>
R8C4 can only be <3>
R5C5 can only be <3>
R9C9 can only be <1>
R5C8 can only be <4>
R8C5 can only be <7>
R5C2 can only be <7>
R6C8 can only be <5>
R6C9 can only be <7>
R1C8 can only be <1>
R9C8 can only be <3>
R1C9 can only be <5>
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