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Common Answers

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Sudoku Solution Path

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R1C5 can only be <5>
R8C6 can only be <9>
R2C5 can only be <8>
R2C4 can only be <6>
R8C4 can only be <1>
R6C6 can only be <4>
R2C6 can only be <2>
R4C4 can only be <9>
R4C2 can only be <4>
R6C8 can only be <9>
R4C6 can only be <6>
R5C5 can only be <1>
R6C2 can only be <1>
R5C9 can only be <3>
R8C5 can only be <7>
R6C4 can only be <8>
R9C5 can only be <4>
R4C8 can only be <7>
R5C8 can only be <4>
R1C7 is the only square in row 1 that can be <4>
R2C3 is the only square in row 2 that can be <1>
R3C3 is the only square in row 3 that can be <7>
R3C9 is the only square in row 3 that can be <8>
R7C3 is the only square in row 7 that can be <4>
R7C7 is the only square in row 7 that can be <7>
R8C3 is the only square in column 3 that can be <3>
R7C8 is the only square in row 7 that can be <3>
R2C8 can only be <5>
R8C7 is the only square in column 7 that can be <5>
Squares R9C3 and R9C7 in row 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R9C1 - removing <29> from <1269> leaving <16>
   R9C9 - removing <9> from <169> leaving <16>
Intersection of row 1 with block 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R3C1 - removing <2> from <256> leaving <56>
   R3C2 - removing <2> from <2356> leaving <356>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 9 can be removed.
   R3C1 - removing <6> from <56> leaving <5>
R7C2 is the only square in row 7 that can be <5>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R1C1=<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
   R1C1 - removing <26> from <269> leaving <9>
R1C3 can only be <2>
R1C9 can only be <6>
R5C1 can only be <2>
R7C1 can only be <1>
R2C2 can only be <3>
R9C3 can only be <9>
R9C9 can only be <1>
R3C8 can only be <2>
R2C7 can only be <9>
R3C2 can only be <6>
R9C7 can only be <2>
R8C2 can only be <2>
R3C7 can only be <3>
R8C8 can only be <6>
R5C2 can only be <9>
R7C9 can only be <9>
R9C1 can only be <6>


 

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