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Common Answers

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Sudoku Solution Path

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R3C4 can only be <2>
R4C5 can only be <8>
R4C7 can only be <7>
R5C6 can only be <6>
R6C3 can only be <2>
R6C5 can only be <9>
R7C4 can only be <6>
R4C3 can only be <5>
R5C8 can only be <2>
R5C4 can only be <5>
R5C9 can only be <9>
R5C5 can only be <1>
R6C7 can only be <3>
R3C7 can only be <9>
R7C7 can only be <4>
R2C8 is the only square in row 2 that can be <5>
R8C2 is the only square in row 8 that can be <9>
R9C7 is the only square in row 9 that can be <6>
R1C7 can only be <2>
R1C5 is the only square in row 1 that can be <6>
R2C9 is the only square in row 2 that can be <6>
R9C2 is the only square in row 9 that can be <2>
R2C1 is the only square in row 2 that can be <2>
R8C9 is the only square in row 8 that can be <2>
Squares R5C1 and R8C1 in column 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C1 - removing <7> from <178> leaving <18>
   R7C1 - removing <7> from <178> leaving <18>
Squares R3C3 and R3C6 in row 3 and R7C3 and R7C6 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 6 can be removed.
   R9C3 - removing <7> from <478> leaving <48>
Squares R1C3 and R9C3 in column 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C3 - removing <8> from <178> leaving <17>
   R7C3 - removing <8> from <178> leaving <17>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R8C5=<34>
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
   R8C5 - removing <34> from <347> leaving <7>
R8C1 can only be <4>
R8C8 can only be <3>
R2C5 can only be <3>
R9C5 can only be <4>
R7C6 can only be <3>
R1C8 can only be <8>
R7C9 can only be <8>
R9C3 can only be <8>
R1C3 can only be <4>
R9C8 can only be <7>
R3C9 can only be <3>
R2C2 can only be <7>
R3C6 can only be <7>
R3C3 can only be <1>
R7C1 can only be <1>
R5C1 can only be <7>
R1C2 can only be <3>
R5C2 can only be <4>
R3C1 can only be <8>
R7C3 can only be <7>


 

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