Mar 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C5 can only be <4>
R1C7 is the only square in row 1 that can be <4>
R1C8 is the only square in row 1 that can be <3>
R3C2 is the only square in row 3 that can be <8>
R2C4 is the only square in row 2 that can be <8>
R4C3 is the only square in row 4 that can be <8>
R5C8 is the only square in row 5 that can be <8>
R6C7 is the only square in row 6 that can be <3>
R7C1 is the only square in row 7 that can be <3>
R9C3 is the only square in row 9 that can be <4>
R5C1 is the only square in row 5 that can be <4>
R8C9 is the only square in row 8 that can be <4>
R9C2 is the only square in row 9 that can be <7>
R9C7 is the only square in row 9 that can be <6>
R2C1 is the only square in column 1 that can be <5>
R5C4 is the only square in column 4 that can be <9>
R5C6 is the only square in row 5 that can be <3>
R8C4 is the only square in row 8 that can be <3>
R8C6 is the only square in row 8 that can be <5>
R9C4 can only be <1>
R9C6 can only be <2>
R1C4 can only be <5>
R9C8 can only be <5>
R1C6 can only be <1>
R7C5 can only be <6>
R2C6 can only be <9>
R3C5 can only be <2>
R3C8 can only be <9>
R7C8 can only be <2>
R7C2 can only be <1>
R8C7 can only be <1>
R7C9 can only be <9>
R4C7 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <9>
Squares R1C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <2> from <127> leaving <17>
R5C3 - removing <26> from <1267> leaving <17>
Squares R3C1 and R3C9 in row 3 and R6C1 and R6C9 in row 6 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 9 can be removed.
R2C9 - removing <7> from <127> leaving <12>
R5C9 - removing <7> from <2567> leaving <256>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R5C9=<56>
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
R5C9 - removing <56> from <256> leaving <2>
R5C2 can only be <6>
R5C7 can only be <7>
R2C9 can only be <1>
R4C9 can only be <5>
R2C3 can only be <7>
R3C9 can only be <7>
R3C1 can only be <1>
R6C9 can only be <6>
R2C7 can only be <2>
R4C5 can only be <1>
R1C2 can only be <2>
R6C1 can only be <7>
R5C3 can only be <1>
R1C3 can only be <6>
R8C3 can only be <2>
R4C1 can only be <2>
R8C1 can only be <6>
R5C5 can only be <5>
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