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Common Answers

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Sudoku Solution Path

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R5C5 can only be <9>
R5C7 can only be <6>
R7C2 can only be <6>
R5C1 can only be <2>
R5C3 can only be <5>
R5C9 can only be <4>
R4C2 can only be <1>
R4C1 can only be <6>
R3C2 can only be <3>
R6C2 can only be <9>
R8C2 can only be <2>
R6C1 can only be <7>
R2C2 can only be <4>
R2C8 is the only square in row 2 that can be <2>
R4C8 can only be <3>
R4C9 can only be <2>
R3C5 is the only square in row 3 that can be <7>
R9C6 is the only square in row 9 that can be <7>
R9C5 is the only square in row 9 that can be <6>
R1C6 is the only square in row 1 that can be <6>
R2C3 is the only square in row 2 that can be <6>
R3C8 is the only square in row 3 that can be <6>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
   R6C9 - removing <1> from <18> leaving <8>
R6C8 can only be <1>
Squares R7C8 and R8C8 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C7 - removing <8> from <378> leaving <37>
   R8C7 - removing <8> from <178> leaving <17>
Squares R8C4<589>, R8C6<89> and R8C8<58> in row 8 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R8C3 - removing <8> from <178> leaving <17>
Squares R1C1 and R1C4 in row 1 and R9C1 and R9C4 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 4 can be removed.
   R2C4 - removing <8> from <389> leaving <39>
   R8C4 - removing <8> from <589> leaving <59>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C4=<58>
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
   R1C4 - removing <58> from <358> leaving <3>
R1C5 can only be <5>
R1C9 can only be <1>
R2C4 can only be <9>
R9C4 can only be <8>
R7C5 can only be <3>
R1C1 can only be <8>
R9C9 can only be <3>
R3C7 can only be <8>
R2C6 can only be <8>
R8C4 can only be <5>
R2C7 can only be <3>
R8C6 can only be <9>
R7C7 can only be <7>
R3C3 can only be <1>
R7C3 can only be <8>
R8C7 can only be <1>
R8C8 can only be <8>
R8C3 can only be <7>
R7C8 can only be <5>
R9C1 can only be <1>


 

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