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Daily Sudoku Answer 



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May 21 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s286363



Reasoning 



R1C1 can only be <7>

R6C1 can only be <1>

R1C6 is the only square in row 1 that can be <3>

R2C2 is the only square in row 2 that can be <3>

R2C3 is the only square in row 2 that can be <4>

R2C8 is the only square in row 2 that can be <9>

R4C8 is the only square in row 4 that can be <3>

R6C8 is the only square in row 6 that can be <5>

R3C8 can only be <1>

R3C5 can only be <8>

R3C7 can only be <5>

R1C4 can only be <6>

R2C7 can only be <6>

R1C9 can only be <8>

R2C5 can only be <1>

R2C6 can only be <2>

R2C4 can only be <5>

R8C7 can only be <1>

R7C7 can only be <2>

R5C7 can only be <8>

R7C3 is the only square in row 7 that can be <1>

R7C2 is the only square in row 7 that can be <8>

R8C5 is the only square in row 8 that can be <3>

Squares R4C6 and R9C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R6C6 - removing <6> from <678> leaving <78>

R8C6 - removing <6> from <678> leaving <78>

Intersection of row 5 with block 4. The value <2> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.

R4C2 - removing <2> from <2469> leaving <469>

R6C2 - removing <2> from <267> leaving <67>

Intersection of block 7 with row 8. The value <6> only appears in one or more of squares R8C1, R8C2 and R8C3 of block 7. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.

R8C8 - removing <6> from <467> leaving <47>

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

R4C2 - removing <4> from <469> leaving <69>

Squares R5C5 and R7C5 in column 5 and R5C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 5 and 7 can be removed.

R5C2 - removing <6> from <2467> leaving <247>

R5C3 - removing <6> from <26> leaving <2>

R3C3 can only be <9>

R3C2 can only be <2>

R8C3 can only be <6>

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

R4C9=<24>

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

R4C9 - removing <24> from <246> leaving <6>

R4C2 can only be <9>

R4C6 can only be <1>

R6C9 can only be <2>

R9C9 can only be <4>

R5C8 can only be <4>

R5C2 can only be <7>

R8C8 can only be <7>

R6C4 can only be <8>

R8C6 can only be <8>

R7C8 can only be <6>

R9C1 can only be <9>

R4C1 can only be <4>

R8C2 can only be <4>

R4C4 can only be <2>

R9C6 can only be <6>

R5C5 can only be <6>

R6C2 can only be <6>

R7C5 can only be <7>

R6C6 can only be <7>

R8C4 can only be <9>

R9C4 can only be <1>



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