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Common Answers

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Sudoku Solution Path

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R2C7 can only be <7>
R3C4 can only be <7>
R9C9 can only be <5>
R2C9 can only be <9>
R4C7 can only be <6>
R6C7 can only be <4>
R4C3 can only be <3>
R6C8 can only be <3>
R5C7 can only be <8>
R4C8 can only be <5>
R9C8 can only be <6>
R5C9 can only be <7>
R8C7 can only be <1>
R8C6 can only be <3>
R2C6 can only be <5>
R6C3 is the only square in row 6 that can be <9>
R7C8 is the only square in row 7 that can be <4>
R1C8 can only be <8>
R8C9 can only be <8>
R1C9 can only be <4>
R3C8 can only be <2>
R3C2 can only be <8>
R7C4 is the only square in row 7 that can be <8>
R8C3 is the only square in row 8 that can be <4>
R1C1 is the only square in column 1 that can be <9>
Squares R4C5<17>, R6C5<27> and R9C5<12> in column 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <127>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R5C5 - removing <12> from <1234> leaving <34>
   R7C5 - removing <1> from <169> leaving <69>
Squares R6C2 and R9C2 in column 2 and R6C5 and R9C5 in column 5 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 6 and 9 can be removed.
   R9C1 - removing <2> from <123> leaving <13>
Squares R2C4 (XY), R5C4 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R5C3 - removing <2> from <26> leaving <6>
R2C3 can only be <2>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
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
   R9C2 - removing <23> from <123> leaving <1>
R9C1 can only be <3>
R9C5 can only be <2>
R4C2 can only be <7>
R7C2 can only be <6>
R6C5 can only be <7>
R8C4 can only be <6>
R4C5 can only be <1>
R6C2 can only be <2>
R5C6 can only be <4>
R5C5 can only be <3>
R3C6 can only be <9>
R5C1 can only be <1>
R7C5 can only be <9>
R1C2 can only be <3>
R8C1 can only be <2>
R7C6 can only be <1>
R3C5 can only be <4>
R2C4 can only be <3>
R2C1 can only be <6>
R1C5 can only be <6>
R5C4 can only be <2>


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