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Common Answers

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Sudoku Solution Path

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R8C5 can only be <4>
R9C5 can only be <3>
R7C6 can only be <9>
R7C4 can only be <6>
R1C7 is the only square in row 1 that can be <4>
R1C1 is the only square in row 1 that can be <9>
R1C3 is the only square in row 1 that can be <3>
R3C2 can only be <8>
R2C5 is the only square in row 2 that can be <8>
R3C7 is the only square in row 3 that can be <3>
R4C4 is the only square in row 4 that can be <9>
R6C6 is the only square in row 6 that can be <3>
R6C5 is the only square in row 6 that can be <7>
R9C7 is the only square in row 9 that can be <9>
R9C9 is the only square in row 9 that can be <1>
R3C8 is the only square in row 3 that can be <1>
R5C4 is the only square in row 5 that can be <1>
R7C7 is the only square in column 7 that can be <8>
R7C9 is the only square in column 9 that can be <7>
Intersection of block 3 with column 9. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
   R5C9 - removing <2> from <256> leaving <56>
Squares R5C5<256>, R5C8<25> and R5C9<56> in row 5 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <256>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R5C6 - removing <5> from <458> leaving <48>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
   R3C3 - removing <5> from <567> leaving <67>
   R4C7 - removing <5> from <156> leaving <16>
   R7C3 - removing <5> from <245> leaving <24>
Intersection of row 4 with block 5. The value <5> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. 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 <5> from <256> leaving <26>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R3C9=<26>
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
   R3C9 - removing <26> from <256> leaving <5>
R3C1 can only be <7>
R3C6 can only be <4>
R1C9 can only be <2>
R5C9 can only be <6>
R2C7 can only be <6>
R5C5 can only be <2>
R4C7 can only be <1>
R1C5 can only be <5>
R2C3 can only be <5>
R3C3 can only be <6>
R9C1 can only be <8>
R3C4 can only be <2>
R5C6 can only be <8>
R4C3 can only be <8>
R6C7 can only be <2>
R5C8 can only be <5>
R6C4 can only be <4>
R5C1 can only be <3>
R4C6 can only be <5>
R7C8 can only be <2>
R6C3 can only be <1>
R8C7 can only be <5>
R7C3 can only be <4>
R8C3 can only be <2>
R9C3 can only be <7>
R4C5 can only be <6>
R5C2 can only be <4>
R7C1 can only be <5>
R7C2 can only be <3>


 

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