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Sudoku Solution Path

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R7C4 is the only square in row 7 that can be <4>
R7C3 is the only square in row 7 that can be <7>
R2C5 is the only square in row 2 that can be <7>
R1C1 is the only square in row 1 that can be <7>
R5C7 is the only square in row 5 that can be <7>
R4C4 is the only square in row 4 that can be <7>
R9C1 is the only square in row 9 that can be <2>
R4C1 can only be <6>
R6C1 can only be <4>
R5C1 can only be <3>
R5C2 can only be <2>
R5C3 can only be <9>
R4C6 is the only square in row 4 that can be <2>
R3C5 is the only square in row 3 that can be <2>
R5C8 is the only square in row 5 that can be <4>
R3C7 is the only square in row 3 that can be <4>
R7C7 is the only square in row 7 that can be <2>
R3C2 is the only square in column 2 that can be <1>
R8C2 is the only square in column 2 that can be <5>
R8C8 is the only square in column 8 that can be <1>
R9C5 is the only square in row 9 that can be <1>
R9C6 is the only square in row 9 that can be <5>
R1C5 is the only square in row 1 that can be <5>
R3C8 is the only square in row 3 that can be <5>
Intersection of row 2 with block 1. The value <6> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R3C3 - removing <6> from <368> leaving <38>
Intersection of row 2 with block 3. The value <9> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R1C9 - removing <9> from <389> leaving <38>
Squares R1C9 and R9C9 in column 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 column.
   R5C9 - removing <8> from <68> leaving <6>
   R6C9 - removing <8> from <1689> leaving <169>
R5C5 can only be <8>
R6C7 is the only square in row 6 that can be <8>
R6C3 is the only square in row 6 that can be <5>
R4C3 can only be <1>
R4C9 can only be <9>
R4C7 can only be <5>
R6C9 can only be <1>
Squares R7C5 and R8C5 in block 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C6 - removing <69> from <3689> leaving <38>
Squares R1C9 and R7C6 form a remote locked pair. <38> can be removed from any square that is common to their groups.
   R1C6 - removing <38> from <389> leaving <9>
R6C6 can only be <6>
R6C4 can only be <9>
R3C4 is the only square in row 3 that can be <6>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R2C3=<68>
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
   R2C3 - removing <68> from <368> leaving <3>
R2C2 can only be <6>
R2C7 can only be <9>
R3C3 can only be <8>
R8C3 can only be <6>
R2C8 can only be <8>
R8C7 can only be <3>
R7C8 can only be <9>
R1C9 can only be <3>
R3C6 can only be <3>
R7C6 can only be <8>
R1C4 can only be <8>
R9C4 can only be <3>
R7C5 can only be <6>
R8C5 can only be <9>
R7C2 can only be <3>
R9C9 can only be <8>


 

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