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Sudoku Solution Path

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R9C4 can only be <7>
R9C6 can only be <3>
R2C2 is the only square in row 2 that can be <2>
R2C8 is the only square in row 2 that can be <3>
R2C7 is the only square in row 2 that can be <8>
R3C8 is the only square in row 3 that can be <4>
R6C2 is the only square in row 6 that can be <8>
R9C2 can only be <6>
R9C8 can only be <8>
R1C4 is the only square in row 1 that can be <6>
R2C1 is the only square in row 2 that can be <6>
R2C3 is the only square in row 2 that can be <7>
R6C5 is the only square in row 6 that can be <4>
R4C2 is the only square in row 4 that can be <4>
R6C8 is the only square in row 6 that can be <6>
R5C5 is the only square in row 5 that can be <6>
R7C3 is the only square in row 7 that can be <8>
R8C8 is the only square in row 8 that can be <2>
R8C2 is the only square in row 8 that can be <3>
R8C7 is the only square in row 8 that can be <6>
R8C5 is the only square in row 8 that can be <8>
Squares R8C4 and R8C6 in row 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R8C9 - removing <1> from <179> leaving <79>
Intersection of row 3 with block 1. The value <5> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R1C2 - removing <5> from <159> leaving <19>
Intersection of block 5 with row 5. The value <9> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
   R5C2 - removing <9> from <579> leaving <57>
   R5C8 - removing <9> from <1579> leaving <157>
Intersection of block 4 with column 1. The value <9> only appears in one or more of squares R4C1, R5C1 and R6C1 of block 4. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
   R8C1 - removing <9> from <579> leaving <57>
Squares R2C5 and R4C5 in column 5 and R2C9 and R4C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 2 and 4 can be removed.
   R2C4 - removing <1> from <149> leaving <49>
   R2C6 - removing <1> from <1459> leaving <459>
   R4C8 - removing <1> from <1579> leaving <579>
Squares R5C2 and R5C8 in row 5 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
   R4C8 - removing <7> from <579> leaving <59>
Squares R4C8 and R6C9 in block 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C9 - removing <59> from <1579> leaving <17>
   R5C8 - removing <5> from <157> leaving <17>
Squares R8C1 (XY), R6C1 (XZ) and R8C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R6C9 - removing <9> from <59> leaving <5>
R6C1 can only be <9>
R4C8 can only be <9>
R1C8 is the only square in column 8 that can be <5>
Squares R1C6 (XY), R8C6 (XZ) and R2C4 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R2C6 - removing <4> from <459> leaving <59>
   R8C4 - removing <4> from <14> leaving <1>
R8C6 can only be <4>
R5C4 can only be <9>
R2C4 can only be <4>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R3C2=<15>
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
   R3C2 - removing <15> from <159> leaving <9>
R3C3 can only be <5>
R3C7 can only be <1>
R1C2 can only be <1>
R7C2 can only be <7>
R8C3 can only be <9>
R7C7 can only be <9>
R2C9 can only be <9>
R7C8 can only be <1>
R5C2 can only be <5>
R8C1 can only be <5>
R8C9 can only be <7>
R5C8 can only be <7>
R4C1 can only be <7>
R4C9 can only be <1>
R1C6 can only be <9>
R2C6 can only be <5>
R2C5 can only be <1>
R5C6 can only be <1>
R4C5 can only be <5>


 

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