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Daily Sudoku Answer 



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Aug 13 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s337236



Reasoning 



R1C3 can only be <4>

R1C7 can only be <6>

R2C2 can only be <8>

R3C1 can only be <3>

R9C7 can only be <5>

R5C3 can only be <9>

R9C3 can only be <3>

R1C1 can only be <1>

R5C7 can only be <3>

R5C5 is the only square in row 5 that can be <1>

R5C9 is the only square in row 5 that can be <6>

R5C6 is the only square in row 5 that can be <2>

R6C6 can only be <8>

R1C5 is the only square in row 1 that can be <2>

R1C4 is the only square in row 1 that can be <8>

R5C1 is the only square in row 5 that can be <8>

R6C9 is the only square in row 6 that can be <2>

R6C5 is the only square in row 6 that can be <6>

R7C5 is the only square in row 7 that can be <3>

R4C6 is the only square in row 4 that can be <3>

R8C5 is the only square in row 8 that can be <8>

R9C1 is the only square in row 9 that can be <2>

R9C9 is the only square in row 9 that can be <8>

Intersection of column 4 with block 5. The value <5> 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 this value.

R4C5 - removing <5> from <4579> leaving <479>

Squares R5C2 and R8C2 in column 2 and R5C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 5 and 8 can be removed.

R5C4 - removing <4> from <457> leaving <57>

Squares R5C2 (XY), R6C1 (XZ) and R5C4 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.

R6C4 - removing <5> from <45> leaving <4>

R6C1 can only be <5>

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

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

R4C4=<59>

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

R4C4 - removing <59> from <579> leaving <7>

R4C1 can only be <4>

R4C5 can only be <9>

R5C4 can only be <5>

R9C4 can only be <9>

R3C5 can only be <5>

R5C8 can only be <4>

R5C2 can only be <7>

R8C8 can only be <7>

R4C9 can only be <5>

R8C2 can only be <4>

R2C8 can only be <5>

R7C9 can only be <4>

R9C6 can only be <7>

R1C6 can only be <9>

R1C9 can only be <7>

R2C5 can only be <7>

R3C9 can only be <9>

R7C1 can only be <7>



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