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Sudoku Solution Path

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R1C8 is the only square in row 1 that can be <2>
R5C4 is the only square in row 5 that can be <6>
R9C3 is the only square in row 9 that can be <2>
R9C8 is the only square in row 9 that can be <7>
R8C5 is the only square in row 8 that can be <7>
R9C9 is the only square in row 9 that can be <3>
Intersection of row 9 with block 7. The value <4> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
   R7C1 - removing <4> from <1458> leaving <158>
   R7C2 - removing <4> from <145689> leaving <15689>
Intersection of block 8 with row 7. The values <349> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
   R7C2 - removing <9> from <15689> leaving <1568>
   R7C8 - removing <9> from <1569> leaving <156>
   R7C9 - removing <9> from <1589> leaving <158>
Intersection of block 4 with column 2. The value <8> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain this value.
   R1C2 - removing <8> from <1458> leaving <145>
   R2C2 - removing <8> from <13568> leaving <1356>
   R3C2 - removing <8> from <135678> leaving <13567>
   R7C2 - removing <8> from <1568> leaving <156>
   R8C2 - removing <8> from <1689> leaving <169>
Squares R3C4<58>, R3C5<1258>, R3C6<12> and R3C9<158> in row 3 form a comprehensive locked quad. These 4 squares can only contain the 4 possibilities <1258>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C1 - removing <158> from <1578> leaving <7>
   R3C2 - removing <15> from <13567> leaving <367>
   R3C8 - removing <15> from <1356> leaving <36>
R5C1 can only be <4>
R5C3 can only be <3>
R9C1 can only be <5>
R6C2 can only be <8>
R4C2 can only be <7>
R9C7 can only be <9>
R9C2 can only be <4>
R4C6 can only be <2>
R3C6 can only be <1>
R1C3 is the only square in row 1 that can be <4>
R1C9 is the only square in row 1 that can be <9>
R3C5 is the only square in row 3 that can be <2>
R5C6 is the only square in row 5 that can be <7>
R5C5 is the only square in row 5 that can be <9>
R7C5 can only be <4>
R6C6 can only be <3>
R6C4 can only be <4>
R7C6 can only be <9>
R7C4 can only be <3>
R6C5 can only be <1>
R6C8 can only be <9>
R4C8 is the only square in row 4 that can be <4>
R8C2 is the only square in row 8 that can be <9>
Intersection of row 8 with block 9. The value <1> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R7C8 - removing <1> from <156> leaving <56>
   R7C9 - removing <1> from <158> leaving <58>
R5C9 is the only square in column 9 that can be <1>
R5C7 can only be <5>
R1C2 is the only square in row 1 that can be <5>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
   R2C2 - removing <6> from <136> leaving <13>
   R2C8 - removing <6> from <1356> leaving <135>
   R8C8 - removing <6> from <16> leaving <1>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R2C7=<16>
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
   R2C7 - removing <16> from <168> leaving <8>
R2C3 can only be <6>
R2C5 can only be <5>
R1C7 can only be <1>
R8C7 can only be <6>
R3C9 can only be <5>
R3C4 can only be <8>
R7C9 can only be <8>
R2C8 can only be <3>
R7C1 can only be <1>
R8C3 can only be <8>
R7C8 can only be <5>
R1C1 can only be <8>
R3C2 can only be <3>
R4C5 can only be <8>
R2C2 can only be <1>
R3C8 can only be <6>
R4C4 can only be <5>
R7C2 can only be <6>

 

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