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Daily Sudoku Answer 



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Jan 22 - Super Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R4C3 can only be <9>

R7C5 can only be <2>

R8C3 can only be <2>

R4C6 can only be <3>

R7C9 can only be <1>

R7C1 can only be <8>

R9C8 can only be <2>

R1C8 can only be <1>

R1C2 can only be <5>

R5C8 can only be <6>

R9C2 can only be <1>

R5C2 can only be <8>

R1C3 is the only square in row 1 that can be <4>

R1C7 is the only square in row 1 that can be <8>

R1C9 is the only square in row 1 that can be <2>

R3C1 is the only square in row 3 that can be <1>

R5C1 can only be <3>

R6C6 is the only square in row 6 that can be <6>

R1C6 can only be <9>

R5C6 can only be <4>

R9C6 can only be <8>

R9C5 is the only square in row 9 that can be <4>

Intersection of column 4 with block 5. The values <25> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.

R5C5 - removing <5> from <579> leaving <79>

Squares R5C5 and R5C9 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R5C4 - removing <79> from <2579> leaving <25>

R5C7 - removing <79> from <1279> leaving <12>

Squares R3C5 and R3C9 in row 3 and R5C5 and R5C9 in row 5 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 5 and 9 can be removed.

R1C5 - removing <7> from <367> leaving <36>

R2C5 - removing <7> from <567> leaving <56>

The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:

R9C7=<35>

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

R9C7 - removing <35> from <359> leaving <9>

R9C4 can only be <3>

R9C9 can only be <5>

R6C7 can only be <1>

R8C7 can only be <3>

R3C9 can only be <7>

R3C5 can only be <5>

R5C9 can only be <9>

R2C7 can only be <5>

R5C5 can only be <7>

R6C3 can only be <5>

R5C7 can only be <2>

R8C5 can only be <9>

R1C4 can only be <7>

R1C1 can only be <6>

R4C4 can only be <2>

R2C5 can only be <6>

R4C7 can only be <7>

R5C4 can only be <5>

R5C3 can only be <1>

R6C4 can only be <9>

R1C5 can only be <3>

R9C1 can only be <7>

R2C3 can only be <7>

R9C3 can only be <6>



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