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Daily Sudoku Answer 



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Aug 06 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s212658



Reasoning 



R7C2 can only be <6>

R2C2 is the only square in row 2 that can be <5>

R2C3 is the only square in row 2 that can be <3>

R5C3 can only be <2>

R5C1 can only be <6>

R8C3 can only be <9>

R4C4 is the only square in row 4 that can be <5>

R5C6 is the only square in row 5 that can be <9>

Squares R8C4 and R9C5 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R8C6 - removing <68> from <3678> leaving <37>

Squares R7C8<37>, R8C7<47> and R8C9<34> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <347>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R8C8 - removing <347> from <23467> leaving <26>

Squares R2C4 and R5C4 in column 4 and R2C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 2 and 5 can be removed.

R2C1 - removing <1> from <12> leaving <2>

R5C5 - removing <1> from <1348> leaving <348>

R2C8 - removing <1> from <1478> leaving <478>

R8C1 can only be <1>

R3C5 is the only square in row 3 that can be <2>

R6C4 is the only square in row 6 that can be <2>

Squares R3C2, R3C8, R1C2 and R1C8 form a Type-1 Unique Rectangle on <19>.

R1C8 - removing <19> from <189> leaving <8>

R1C5 can only be <1>

R1C2 can only be <9>

R3C2 can only be <1>

R3C8 can only be <9>

R2C9 is the only square in row 2 that can be <1>

R4C8 is the only square in row 4 that can be <1>

R5C4 is the only square in row 5 that can be <1>

R5C7 is the only square in column 7 that can be <8>

Squares R6C2 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R6C5 - removing <34> from <3478> leaving <78>

R6C6 - removing <3> from <378> leaving <78>

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

R4C5=<46>

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

R4C5 - removing <46> from <346> leaving <3>

R4C2 can only be <4>

R4C6 can only be <6>

R5C5 can only be <4>

R7C5 can only be <7>

R2C6 can only be <8>

R5C9 can only be <3>

R8C9 can only be <4>

R6C8 can only be <4>

R6C2 can only be <3>

R2C8 can only be <7>

R7C8 can only be <3>

R6C5 can only be <8>

R8C6 can only be <3>

R8C7 can only be <7>

R2C4 can only be <6>

R6C6 can only be <7>

R2C7 can only be <4>

R9C5 can only be <6>

R9C8 can only be <2>

R8C4 can only be <8>

R9C2 can only be <8>

R8C8 can only be <6>

R8C2 can only be <2>



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