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Sudoku Solution Path

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R3C5 is the only square in row 3 that can be <3>
R3C1 is the only square in row 3 that can be <5>
R1C6 is the only square in row 1 that can be <5>
R1C4 is the only square in row 1 that can be <6>
R5C7 is the only square in row 5 that can be <3>
R4C1 is the only square in row 4 that can be <3>
R4C2 is the only square in row 4 that can be <1>
R2C8 is the only square in row 2 that can be <1>
R3C7 can only be <9>
R3C9 can only be <4>
R3C3 can only be <1>
R2C2 is the only square in row 2 that can be <2>
R8C2 can only be <4>
R8C4 can only be <3>
R6C2 can only be <8>
R5C2 can only be <7>
R2C6 is the only square in row 2 that can be <7>
R8C6 is the only square in row 8 that can be <1>
R9C9 is the only square in row 9 that can be <3>
R4C9 is the only square in column 9 that can be <9>
Squares R5C3 and R5C6 in row 5 form a simple locked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C4 - removing <4> from <489> leaving <89>
   R5C5 - removing <46> from <45689> leaving <589>
   R5C8 - removing <6> from <568> leaving <58>
Squares R4C5<68>, R7C5<268> and R8C5<26> in column 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <268>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R5C5 - removing <8> from <589> leaving <59>
   R6C5 - removing <6> from <456> leaving <45>
Squares R4C5 and R4C8 in row 4 and R8C5 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 8 can be removed.
   R6C8 - removing <6> from <256> leaving <25>
   R7C5 - removing <6> from <268> leaving <28>
Squares R6C1 and R9C6 form a remote locked pair. <46> can be removed from any square that is common to their groups.
   R9C1 - removing <6> from <16> leaving <1>
R7C7 is the only square in row 7 that can be <1>
Squares R5C3 and R5C6 in row 5 and R9C3 and R9C6 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 6 can be removed.
   R7C3 - removing <6> from <267> leaving <27>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R7C9=<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
   R7C9 - removing <68> from <268> leaving <2>
R7C3 can only be <7>
R7C5 can only be <8>
R1C9 can only be <8>
R6C9 can only be <6>
R8C8 can only be <6>
R9C7 can only be <8>
R8C5 can only be <2>
R4C8 can only be <8>
R9C4 can only be <4>
R1C7 can only be <2>
R4C5 can only be <6>
R5C8 can only be <5>
R5C5 can only be <9>
R6C8 can only be <2>
R6C1 can only be <4>
R7C1 can only be <6>
R1C3 can only be <4>
R9C6 can only be <6>
R2C4 can only be <9>
R9C3 can only be <2>
R5C6 can only be <4>
R1C1 can only be <7>
R5C3 can only be <6>
R2C5 can only be <4>
R5C4 can only be <8>
R6C5 can only be <5>


 

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