Sep 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C4 can only be <4>
R9C6 can only be <9>
R6C6 can only be <4>
R8C5 can only be <3>
R7C5 can only be <8>
R1C7 is the only square in row 1 that can be <3>
R1C4 is the only square in row 1 that can be <1>
R4C4 can only be <5>
R4C1 can only be <9>
R6C4 can only be <7>
R5C4 can only be <8>
R6C1 can only be <5>
R5C6 can only be <3>
R4C6 can only be <6>
R6C9 can only be <1>
R6C5 can only be <9>
R3C9 can only be <2>
R4C9 can only be <3>
R5C8 can only be <4>
R7C9 can only be <5>
R4C5 can only be <1>
R1C6 can only be <8>
R5C7 can only be <5>
R1C3 can only be <6>
R5C5 can only be <2>
R8C8 is the only square in row 8 that can be <7>
Squares R2C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C2 - removing <4> from <347> leaving <37>
R7C2 - removing <4> from <134> leaving <13>
Squares R9C3, R9C7, R7C3 and R7C7 form a Type-4 Unique Rectangle on <12>.
R7C3 - removing <1> from <129> leaving <29>
R7C7 - removing <1> from <1249> leaving <249>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R7C7=<24>
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
R7C7 - removing <24> from <249> leaving <9>
R7C3 can only be <2>
R7C8 can only be <1>
R2C7 can only be <8>
R8C7 can only be <4>
R7C2 can only be <3>
R3C8 can only be <6>
R9C7 can only be <2>
R8C2 can only be <5>
R9C3 can only be <1>
R2C3 can only be <5>
R3C7 can only be <1>
R3C5 can only be <4>
R2C8 can only be <9>
R7C1 can only be <4>
R3C2 can only be <7>
R8C3 can only be <9>
R2C2 can only be <4>
R5C3 can only be <7>
R2C5 can only be <6>
R3C1 can only be <3>
R3C3 can only be <8>
R5C2 can only be <1>
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