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Common Answers

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Sudoku Solution Path

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R3C6 can only be <3>
R4C7 can only be <8>
R8C5 can only be <7>
R1C6 can only be <6>
R5C6 can only be <2>
R4C5 can only be <1>
R6C7 can only be <4>
R7C6 can only be <4>
R9C6 can only be <1>
R2C5 can only be <8>
R2C8 can only be <4>
R2C1 can only be <3>
R2C2 can only be <7>
R2C9 can only be <6>
R1C1 is the only square in row 1 that can be <1>
R1C2 is the only square in row 1 that can be <4>
R5C4 is the only square in row 5 that can be <8>
R7C9 is the only square in row 7 that can be <3>
R9C7 can only be <7>
R1C7 can only be <3>
R8C1 is the only square in row 8 that can be <6>
R4C3 is the only square in row 4 that can be <6>
R8C9 is the only square in row 8 that can be <4>
R9C1 is the only square in row 9 that can be <4>
R9C4 is the only square in row 9 that can be <9>
R7C4 can only be <2>
R7C1 can only be <9>
Intersection of column 8 with block 9. The value <2> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R9C9 - removing <2> from <258> leaving <58>
Squares R5C2 and R5C8 in row 5 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
   R9C2 - removing <5> from <235> leaving <23>
   R9C8 - removing <5> from <258> leaving <28>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C9=<79>
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
   R1C9 - removing <79> from <789> leaving <8>
R1C3 can only be <5>
R1C8 can only be <9>
R3C9 can only be <7>
R9C9 can only be <5>
R3C4 can only be <5>
R9C3 can only be <3>
R4C9 can only be <2>
R8C8 can only be <2>
R1C4 can only be <7>
R3C1 can only be <8>
R5C8 can only be <5>
R6C1 can only be <2>
R4C1 can only be <5>
R6C9 can only be <9>
R5C2 can only be <3>
R6C5 can only be <3>
R8C2 can only be <5>
R9C8 can only be <8>
R9C2 can only be <2>
R6C3 can only be <8>
R5C5 can only be <9>


 

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