Nov 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C2 can only be <6>
R2C5 can only be <1>
R2C8 can only be <5>
R3C7 can only be <3>
R8C8 can only be <4>
R3C9 can only be <7>
R5C8 can only be <3>
R1C1 is the only square in row 1 that can be <3>
R4C5 is the only square in row 4 that can be <7>
R6C5 is the only square in row 6 that can be <3>
R7C9 is the only square in row 7 that can be <3>
R7C1 is the only square in row 7 that can be <7>
R9C3 is the only square in row 9 that can be <1>
R9C1 is the only square in row 9 that can be <5>
R4C3 is the only square in column 3 that can be <5>
Squares R8C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <29> from <2489> leaving <48>
Squares R8C5 and R9C5 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <2> from <268> leaving <68>
R7C6 - removing <9> from <689> leaving <68>
Squares R7C4 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C7 - removing <6> from <269> leaving <29>
Squares R4C4 and R4C7 in row 4, R6C3, R6C4 and R6C7 in row 6 and R7C3 and R7C7 in row 7 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 3, 4 and 7 can be removed.
R3C3 - removing <2> from <248> leaving <48>
R5C4 - removing <2> from <1258> leaving <158>
R9C7 - removing <2> from <269> leaving <69>
R3C1 is the only square in row 3 that can be <2>
R5C1 can only be <4>
R5C5 can only be <8>
R1C5 can only be <4>
R1C3 can only be <8>
R3C3 can only be <4>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R6C7=<14>
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
R6C7 - removing <14> from <124> leaving <2>
R6C3 can only be <9>
R6C4 can only be <1>
R4C7 can only be <4>
R7C7 can only be <9>
R5C9 can only be <1>
R7C3 can only be <2>
R9C7 can only be <6>
R9C9 can only be <2>
R1C7 can only be <1>
R9C5 can only be <9>
R1C9 can only be <6>
R4C6 can only be <6>
R5C4 can only be <5>
R6C6 can only be <4>
R5C2 can only be <2>
R8C2 can only be <9>
R8C5 can only be <2>
R4C4 can only be <2>
R7C6 can only be <8>
R5C6 can only be <9>
R3C4 can only be <8>
R7C4 can only be <6>
R3C6 can only be <5>
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