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Sudoku Solution Path

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R3C3 can only be <6>
R7C3 can only be <3>
R8C3 can only be <4>
R2C3 can only be <2>
R5C5 is the only square in row 5 that can be <1>
R5C2 is the only square in row 5 that can be <3>
R4C4 is the only square in row 4 that can be <3>
R6C8 is the only square in row 6 that can be <5>
R6C2 is the only square in row 6 that can be <6>
R5C1 can only be <4>
R4C2 can only be <2>
R4C6 can only be <9>
R4C8 can only be <4>
R2C6 can only be <8>
R2C4 can only be <7>
R6C6 can only be <2>
R6C4 can only be <8>
R8C6 can only be <6>
R2C1 can only be <5>
R8C4 can only be <2>
R1C5 can only be <3>
R2C5 can only be <9>
R2C2 is the only square in row 2 that can be <4>
R9C1 is the only square in column 1 that can be <6>
R1C2 is the only square in column 2 that can be <1>
Squares R1C9 and R9C9 in column 9 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.
   R8C9 - removing <7> from <179> leaving <19>
Squares R1C8<278>, R3C8<789>, R5C8<69>, R7C8<679> and R9C8<278> in column 8 form a comprehensive locked set. These 5 squares can only contain the 5 possibilities <26789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C8 - removing <6> from <136> leaving <13>
   R8C8 - removing <789> from <13789> leaving <13>
Squares R3C2 and R3C8 in row 3 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.
   R1C8 - removing <7> from <278> leaving <28>
   R8C2 - removing <7> from <5789> leaving <589>
   R9C2 - removing <7> from <578> leaving <58>
   R9C8 - removing <7> from <278> leaving <28>
Squares R1C8 and R9C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C8 - removing <8> from <789> leaving <79>
Squares R3C2 (XY), R7C2 (XZ) and R3C7 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R7C7 - removing <9> from <69> leaving <6>
R2C7 can only be <3>
R2C8 can only be <1>
R2C9 can only be <6>
R8C8 can only be <3>
R5C9 can only be <9>
R5C8 can only be <6>
R8C9 can only be <1>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R8C2=<59>
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
   R8C2 - removing <59> from <589> leaving <8>
R8C1 can only be <7>
R8C7 can only be <9>
R3C2 can only be <7>
R9C2 can only be <5>
R3C7 can only be <8>
R7C8 can only be <7>
R9C5 can only be <7>
R9C9 can only be <2>
R8C5 can only be <5>
R9C8 can only be <8>
R1C9 can only be <7>
R1C1 can only be <8>
R3C8 can only be <9>
R7C2 can only be <9>
R1C8 can only be <2>


 

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