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Sudoku Solution Path

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R9C5 is the only square in row 9 that can be <8>
R2C9 is the only square in row 2 that can be <8>
R9C2 is the only square in row 9 that can be <9>
R7C6 is the only square in column 6 that can be <6>
R4C7 is the only square in column 7 that can be <8>
R6C7 is the only square in column 7 that can be <1>
R6C3 can only be <6>
R9C3 can only be <3>
R9C7 can only be <2>
R9C8 can only be <6>
R1C7 can only be <3>
R7C8 can only be <4>
R8C9 can only be <9>
R8C5 can only be <2>
R7C9 can only be <3>
R8C1 can only be <6>
R3C9 is the only square in row 3 that can be <6>
R5C8 is the only square in column 8 that can be <5>
R7C2 is the only square in column 2 that can be <5>
R7C1 can only be <2>
R3C5 is the only square in column 5 that can be <5>
Squares R3C6 and R5C6 in column 6 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 column.
   R4C6 - removing <1> from <125> leaving <25>
Squares R3C6, R5C6, R3C4 and R5C4 form a Type-4 Unique Rectangle on <18>.
   R3C4 - removing <1> from <1378> leaving <378>
   R5C4 - removing <1> from <13789> leaving <3789>
Squares R3C2 (XY), R3C8 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
   R3C1 - removing <7> from <137> leaving <13>
R2C1 is the only square in column 1 that can be <7>
R2C5 can only be <3>
Squares R4C3 (XY), R4C4 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
   R5C4 - removing <3> from <3789> leaving <789>
   R4C1 - removing <3> from <135> leaving <15>
R4C4 is the only square in row 4 that can be <3>
R7C4 is the only square in column 4 that can be <1>
R7C5 can only be <9>
Intersection of row 4 with block 4. The value <1> only appears in one or more of squares R4C1, R4C2 and R4C3 of row 4. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
   R5C1 - removing <1> from <139> leaving <39>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R5C4=<89>
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
   R5C4 - removing <89> from <789> leaving <7>
R5C5 can only be <1>
R5C9 can only be <4>
R3C4 can only be <8>
R6C4 can only be <9>
R5C6 can only be <8>
R1C5 can only be <7>
R3C6 can only be <1>
R5C2 can only be <3>
R4C9 can only be <2>
R6C1 can only be <5>
R1C8 can only be <2>
R1C2 can only be <4>
R3C8 can only be <7>
R3C1 can only be <3>
R4C6 can only be <5>
R6C9 can only be <7>
R5C1 can only be <9>
R3C2 can only be <2>
R6C6 can only be <2>
R4C1 can only be <1>
R1C3 can only be <1>
R4C3 can only be <4>


 

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