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Sudoku Solution Path

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R1C1 can only be <5>
R1C9 can only be <9>
R8C7 can only be <2>
R9C9 can only be <3>
R1C5 can only be <4>
R9C1 can only be <7>
R5C1 can only be <4>
R7C3 can only be <6>
R8C3 can only be <5>
R9C5 can only be <5>
R5C9 can only be <2>
R7C7 can only be <9>
R7C2 can only be <8>
R7C8 can only be <7>
R7C5 can only be <3>
R8C4 can only be <7>
R8C6 can only be <8>
R7C4 can only be <4>
R7C6 can only be <1>
R3C4 is the only square in row 3 that can be <2>
R3C7 is the only square in row 3 that can be <4>
R3C3 is the only square in row 3 that can be <9>
R2C4 is the only square in row 2 that can be <9>
R4C3 is the only square in row 4 that can be <1>
R4C8 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <2>
R6C6 is the only square in row 6 that can be <4>
R6C7 is the only square in row 6 that can be <8>
R6C2 is the only square in row 6 that can be <6>
Squares R4C4 and R6C4 in block 5 form a simple locked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C6 - removing <5> from <567> leaving <67>
Squares R2C3 and R2C7 in row 2 and R5C3 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
   R4C7 - removing <3> from <356> leaving <56>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R3C6=<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
   R3C6 - removing <56> from <567> leaving <7>
R3C2 can only be <3>
R3C5 can only be <6>
R2C6 can only be <5>
R4C6 can only be <6>
R4C7 can only be <5>
R5C5 can only be <7>
R4C4 can only be <3>
R2C7 can only be <3>
R6C8 can only be <3>
R5C3 can only be <3>
R6C4 can only be <5>
R3C8 can only be <5>
R5C7 can only be <6>
R2C3 can only be <7>
R4C2 can only be <7>


 

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