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 Sudoku Solution Path   R4C4 can only be <7> R4C9 can only be <5> R5C5 can only be <5> R6C9 can only be <1> R4C1 can only be <6> R6C4 can only be <9> R6C6 can only be <6> R5C7 can only be <6> R5C3 can only be <4> R6C1 can only be <7> R4C6 can only be <2> R3C1 is the only square in row 3 that can be <1> R7C7 is the only square in row 7 that can be <1> R9C7 is the only square in row 9 that can be <5> R3C8 is the only square in row 3 that can be <5> Intersection of column 7 with block 3. The values <23> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.    R1C9 - removing <2> from <2489> leaving <489>    R3C9 - removing <2> from <28> leaving <8> R2C3 is the only square in row 2 that can be <8> R2C7 is the only square in row 2 that can be <3> R8C8 is the only square in row 8 that can be <8> R7C1 is the only square in row 7 that can be <8> Squares R3C3 and R3C5 in row 3 and R7C3 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 5 can be removed.    R1C3 - removing <3> from <237> leaving <27>    R9C3 - removing <3> from <237> leaving <27> Squares R1C3 and R9C3 in column 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.    R3C3 - removing <27> from <2367> leaving <36>    R7C3 - removing <27> from <2379> leaving <39>    R8C3 - removing <7> from <679> leaving <69> Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.    R7C9 - removing <4> from <249> leaving <29> Squares R1C3 and R9C3 in column 3 and R1C6 and R9C6 in column 6 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 1 and 9 can be removed.    R1C7 - removing <7> from <279> leaving <29> Squares R9C9 (XY), R9C3 (XZ) and R7C8 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.    R7C2 - removing <7> from <247> leaving <24> The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:    R3C2=<26> 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 <26> from <267> leaving <7> R3C5 can only be <3> R3C7 can only be <2> R2C2 can only be <4> R8C2 can only be <6> R1C3 can only be <2> R3C3 can only be <6> R7C5 can only be <7> R1C4 can only be <8> R1C7 can only be <9> R7C8 can only be <4> R9C6 can only be <8> R7C2 can only be <2> R2C8 can only be <7> R9C9 can only be <2> R8C3 can only be <9> R8C7 can only be <7> R7C3 can only be <3> R9C4 can only be <3> R1C6 can only be <7> R9C3 can only be <7> R7C9 can only be <9> R1C9 can only be <4> R1C1 can only be <3> R9C1 can only be <4>

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