Oct 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <3>
R1C6 can only be <5>
R2C5 can only be <7>
R4C9 can only be <5>
R6C1 can only be <4>
R6C5 can only be <9>
R9C4 can only be <2>
R1C2 can only be <4>
R4C1 can only be <2>
R5C8 can only be <9>
R5C6 can only be <6>
R9C8 can only be <4>
R6C9 can only be <8>
R5C4 can only be <8>
R8C5 can only be <6>
R1C8 can only be <1>
R7C8 can only be <5>
R4C5 can only be <1>
R5C2 can only be <5>
R5C5 can only be <2>
R9C6 can only be <9>
R3C8 can only be <7>
R2C7 is the only square in row 2 that can be <4>
R7C3 is the only square in row 7 that can be <4>
R8C9 is the only square in row 8 that can be <1>
R3C7 is the only square in column 7 that can be <5>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 7 can be removed.
R2C3 - removing <6> from <356> leaving <35>
R7C7 - removing <6> from <2689> leaving <289>
Squares R2C1 (XY), R8C1 (XZ) and R1C3 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R8C3 - removing <9> from <259> leaving <25>
R3C1 - removing <9> from <89> leaving <8>
Squares R7C1 and R7C9 in row 7 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 row.
R7C7 - removing <9> from <289> leaving <28>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R3C3=<29>
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
R3C3 - removing <29> from <239> leaving <3>
R3C2 can only be <2>
R3C9 can only be <9>
R2C3 can only be <5>
R9C3 can only be <6>
R7C9 can only be <6>
R1C7 can only be <6>
R7C1 can only be <9>
R2C9 can only be <3>
R9C7 can only be <8>
R1C3 can only be <9>
R9C2 can only be <3>
R7C7 can only be <2>
R2C1 can only be <6>
R8C3 can only be <2>
R7C2 can only be <8>
R8C1 can only be <5>
R8C7 can only be <9>
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