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Sudoku Solution Path

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R4C9 can only be <3>
R5C4 can only be <6>
R6C9 can only be <8>
R4C1 can only be <6>
R5C2 can only be <3>
R5C6 can only be <7>
R1C4 can only be <1>
R4C5 can only be <1>
R5C5 can only be <5>
R6C5 can only be <4>
R6C1 can only be <7>
R1C6 can only be <6>
R9C4 can only be <4>
R1C5 can only be <7>
R9C6 can only be <1>
R2C5 can only be <8>
R5C1 can only be <8>
R3C3 is the only square in row 3 that can be <7>
R7C2 is the only square in row 7 that can be <4>
R8C7 is the only square in row 8 that can be <7>
R2C2 is the only square in column 2 that can be <2>
R5C8 is the only square in column 8 that can be <2>
R5C9 can only be <9>
Squares R2C3 and R2C8 in row 2 and R8C3 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 8 can be removed.
   R3C8 - removing <1> from <189> leaving <89>
   R7C3 - removing <1> from <13568> leaving <3568>
   R7C8 - removing <1> from <138> leaving <38>
Squares R3C2<69>, R3C7<689> and R3C8<89> in row 3 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <689>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C1 - removing <9> from <159> leaving <15>
   R3C9 - removing <6> from <156> leaving <15>
Intersection of column 9 with block 9. The value <6> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R7C7 - removing <6> from <368> leaving <38>
   R9C7 - removing <6> from <23689> leaving <2389>
Squares R7C7 and R7C8 in row 7 form a simple locked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R7C1 - removing <3> from <135> leaving <15>
   R7C3 - removing <38> from <3568> leaving <56>
R9C3 is the only square in column 3 that can be <8>
Squares R3C1 and R7C1 in column 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R1C1 - removing <5> from <359> leaving <39>
Squares R7C7 and R7C8 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C8 - removing <3> from <139> leaving <19>
   R9C7 - removing <3> from <239> leaving <29>
Squares R1C1 and R1C7 in row 1 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 7 can be removed.
   R3C7 - removing <9> from <689> leaving <68>
Squares R2C7<36>, R3C7<68> and R7C7<38> in column 7 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R1C7 - removing <3> from <239> leaving <29>
Intersection of row 1 with block 1. The value <3> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R2C3 - removing <3> from <136> leaving <16>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R8C3=<13>
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
   R8C3 - removing <13> from <136> leaving <6>
R8C2 can only be <9>
R8C5 can only be <3>
R2C3 can only be <1>
R7C3 can only be <5>
R9C5 can only be <6>
R9C9 can only be <2>
R9C7 can only be <9>
R1C9 can only be <5>
R1C3 can only be <3>
R3C9 can only be <1>
R2C8 can only be <3>
R3C1 can only be <5>
R2C7 can only be <6>
R7C8 can only be <8>
R7C1 can only be <1>
R7C9 can only be <6>
R7C7 can only be <3>
R3C8 can only be <9>
R8C8 can only be <1>
R3C2 can only be <6>
R9C1 can only be <3>
R1C1 can only be <9>
R1C7 can only be <2>
R3C7 can only be <8>


 

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