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Sudoku Solution Path

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R5C5 can only be <5>
R2C4 is the only square in row 2 that can be <2>
R6C9 is the only square in row 6 that can be <6>
R9C3 is the only square in row 9 that can be <2>
R4C2 is the only square in column 2 that can be <9>
R4C7 can only be <5>
R4C8 can only be <2>
R6C8 can only be <1>
R6C3 can only be <8>
R6C7 can only be <3>
R1C8 can only be <5>
R9C8 can only be <9>
R6C2 can only be <5>
R5C7 can only be <9>
R5C9 can only be <4>
R5C3 can only be <1>
R4C9 can only be <8>
R6C1 can only be <2>
R5C1 can only be <3>
R8C9 is the only square in column 9 that can be <3>
Squares R1C2 and R2C1 in block 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R3C1 - removing <1> from <147> leaving <47>
Squares R2C6<89>, R3C6<59> and R8C6<58> in column 6 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R1C6 - removing <8> from <368> leaving <36>
   R7C6 - removing <59> from <5679> leaving <67>
   R9C6 - removing <8> from <378> leaving <37>
R7C4 is the only square in row 7 that can be <9>
R7C1 is the only square in row 7 that can be <5>
Squares R1C2 and R9C2 in column 2 and R1C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 9 can be removed.
   R1C4 - removing <1> from <134> leaving <34>
   R9C4 - removing <1> from <134> leaving <34>
   R1C5 - removing <1> from <1468> leaving <468>
   R9C5 - removing <1> from <148> leaving <48>
Squares R1C4 and R9C4 in column 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C4 - removing <4> from <145> leaving <15>
Intersection of block 2 with row 3. The values <15> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain these values.
   R3C9 - removing <1> from <179> leaving <79>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C5=<68>
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
   R1C5 - removing <68> from <468> leaving <4>
R1C3 can only be <7>
R1C4 can only be <3>
R3C5 can only be <1>
R9C5 can only be <8>
R3C4 can only be <5>
R7C5 can only be <6>
R7C6 can only be <7>
R7C9 can only be <1>
R9C6 can only be <3>
R2C9 can only be <9>
R9C7 can only be <7>
R9C2 can only be <1>
R8C6 can only be <5>
R9C4 can only be <4>
R1C6 can only be <6>
R1C7 can only be <1>
R4C3 can only be <4>
R3C1 can only be <4>
R1C2 can only be <8>
R2C6 can only be <8>
R3C9 can only be <7>
R4C1 can only be <7>
R3C6 can only be <9>
R8C4 can only be <1>
R8C1 can only be <8>
R2C1 can only be <1>


 

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