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Common Answers

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Sudoku Solution Path

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R5C2 can only be <6>
R6C1 can only be <1>
R5C3 can only be <2>
R3C2 can only be <5>
R4C1 can only be <5>
R7C2 can only be <1>
R8C3 can only be <4>
R8C5 can only be <3>
R8C7 can only be <1>
R1C1 is the only square in row 1 that can be <2>
R2C3 is the only square in row 2 that can be <1>
R4C4 is the only square in row 4 that can be <1>
R7C7 is the only square in row 7 that can be <2>
R3C1 is the only square in column 1 that can be <4>
R7C5 is the only square in column 5 that can be <9>
R9C3 is the only square in row 9 that can be <9>
R9C9 is the only square in row 9 that can be <5>
R7C3 is the only square in row 7 that can be <5>
R7C1 is the only square in row 7 that can be <8>
R9C1 can only be <3>
R9C7 is the only square in row 9 that can be <6>
R1C6 is the only square in column 6 that can be <3>
R3C7 is the only square in column 7 that can be <9>
Intersection of row 6 with block 5. The value <8> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
   R5C5 - removing <8> from <478> leaving <47>
Intersection of column 5 with block 2. The value <8> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R1C4 - removing <8> from <478> leaving <47>
Squares R5C5 (XY), R5C8 (XZ) and R3C5 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
   R3C8 - removing <8> from <38> leaving <3>
R7C8 can only be <4>
R7C9 can only be <3>
R5C8 can only be <8>
Squares R2C5 and R2C7 in row 2 and R5C5 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 7 can be removed.
   R1C7 - removing <4> from <478> leaving <78>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C9=<46>
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 <46> from <467> leaving <7>
R1C4 can only be <4>
R1C7 can only be <8>
R3C9 can only be <6>
R6C9 can only be <9>
R3C3 can only be <8>
R6C6 can only be <8>
R4C9 can only be <4>
R9C4 can only be <8>
R2C5 can only be <8>
R1C3 can only be <6>
R2C7 can only be <4>
R3C5 can only be <7>
R5C7 can only be <7>
R5C5 can only be <4>
R4C6 can only be <9>
R6C4 can only be <7>
R9C6 can only be <4>


 

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