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Common Answers

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Sudoku Solution Path

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R2C1 is the only square in row 2 that can be <3>
R5C1 is the only square in row 5 that can be <4>
R4C7 is the only square in row 4 that can be <4>
R1C1 is the only square in column 1 that can be <1>
R4C1 is the only square in column 1 that can be <9>
R3C7 is the only square in column 7 that can be <9>
R1C4 is the only square in row 1 that can be <9>
R2C9 is the only square in block 3 that can be <1>
Squares R1C8 and R1C9 in row 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C2 - removing <8> from <28> leaving <2>
   R1C5 - removing <78> from <25678> leaving <256>
   R1C6 - removing <8> from <2568> leaving <256>
R3C3 can only be <8>
R3C4 can only be <1>
R3C6 can only be <2>
R5C9 is the only square in row 5 that can be <2>
R5C8 is the only square in row 5 that can be <9>
R5C2 is the only square in row 5 that can be <7>
R6C3 is the only square in row 6 that can be <2>
R9C5 is the only square in row 9 that can be <2>
R9C6 is the only square in row 9 that can be <4>
R2C6 can only be <8>
R2C4 can only be <7>
R2C5 can only be <4>
R7C7 is the only square in row 7 that can be <7>
R6C7 can only be <8>
R7C4 is the only square in row 7 that can be <8>
R5C5 is the only square in row 5 that can be <8>
R4C2 is the only square in row 4 that can be <8>
R4C5 is the only square in row 4 that can be <5>
R1C5 can only be <6>
R1C6 can only be <5>
R6C5 can only be <1>
R8C5 can only be <7>
R4C8 is the only square in row 4 that can be <1>
R8C6 is the only square in row 8 that can be <1>
R9C9 is the only square in row 9 that can be <9>
Squares R6C2 and R9C2 in column 2 and R6C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 6 and 9 can be removed.
   R9C4 - removing <3> from <356> leaving <56>
   R6C9 - removing <3> from <367> leaving <67>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R9C1=<68>
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
   R9C1 - removing <68> from <568> leaving <5>
R9C2 can only be <3>
R9C4 can only be <6>
R6C1 can only be <6>
R8C1 can only be <8>
R9C8 can only be <8>
R6C2 can only be <5>
R7C3 can only be <6>
R5C4 can only be <3>
R7C6 can only be <3>
R1C8 can only be <7>
R8C9 can only be <3>
R1C9 can only be <8>
R6C8 can only be <3>
R5C6 can only be <6>
R8C4 can only be <5>
R6C9 can only be <7>
R4C3 can only be <3>
R4C9 can only be <6>


 

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