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Common Answers

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Sudoku Solution Path

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R1C1 can only be <8>
R2C5 can only be <9>
R4C4 can only be <1>
R4C5 can only be <7>
R4C6 can only be <4>
R5C2 can only be <8>
R5C6 can only be <5>
R5C8 can only be <7>
R6C4 can only be <8>
R6C6 can only be <6>
R8C5 can only be <8>
R9C9 can only be <3>
R7C1 can only be <1>
R5C4 can only be <9>
R5C5 can only be <2>
R6C5 can only be <3>
R3C1 can only be <5>
R9C3 can only be <8>
R9C1 can only be <9>
R9C7 can only be <5>
R8C2 is the only square in row 8 that can be <5>
Squares R1C7 and R3C9 in block 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R1C9 - removing <27> from <247> leaving <4>
   R3C7 - removing <27> from <1279> leaving <19>
Squares R1C3 and R1C7 in row 1 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
   R3C3 - removing <7> from <1237> leaving <123>
   R7C3 - removing <7> from <347> leaving <34>
   R7C7 - removing <7> from <278> leaving <28>
Squares R2C8 (XY), R2C2 (XZ) and R7C8 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R7C2 - removing <4> from <347> leaving <37>
R2C2 is the only square in column 2 that can be <4>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
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
   R3C3 - removing <12> from <123> leaving <3>
R3C2 can only be <7>
R3C8 can only be <9>
R2C3 can only be <1>
R7C3 can only be <4>
R3C7 can only be <1>
R8C8 can only be <4>
R7C8 can only be <8>
R8C3 can only be <7>
R7C7 can only be <2>
R2C8 can only be <3>
R8C7 can only be <9>
R1C3 can only be <2>
R7C2 can only be <3>
R1C7 can only be <7>
R3C9 can only be <2>
R2C7 can only be <8>
R7C9 can only be <7>


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