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Daily Sudoku Answer 



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Nov 26 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s243392



Reasoning 



R2C6 can only be <6>

R5C1 can only be <1>

R5C5 can only be <2>

R8C4 can only be <6>

R2C7 can only be <4>

R1C5 can only be <3>

R5C6 can only be <5>

R9C5 can only be <9>

R8C6 can only be <7>

R4C5 can only be <6>

R6C5 can only be <7>

R2C4 can only be <2>

R2C3 can only be <3>

R6C6 can only be <9>

R4C6 can only be <1>

R3C8 is the only square in row 3 that can be <3>

R4C8 is the only square in row 4 that can be <9>

R7C8 can only be <2>

R7C3 can only be <8>

Squares R4C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R8C2 - removing <3> from <12349> leaving <1249>

R9C2 - removing <3> from <1346> leaving <146>

Squares R7C2<69>, R8C1<39> and R9C1<36> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R8C2 - removing <9> from <1249> leaving <124>

R9C2 - removing <6> from <146> leaving <14>

Squares R9C2 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R9C9 - removing <4> from <346> leaving <36>

Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.

R3C2 - removing <1> from <126> leaving <26>

R8C2 - removing <1> from <124> leaving <24>

R8C8 - removing <1> from <145> leaving <45>

Squares R3C2 and R3C7 in row 3 and R7C2 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 7 can be removed.

R1C2 - removing <6> from <156> leaving <15>

Squares R4C2, R4C4, R6C2 and R6C4 form a Type-1 Unique Rectangle on <38>.

R6C4 - removing <38> from <348> leaving <4>

R6C8 can only be <8>

R5C4 can only be <8>

R6C2 can only be <3>

R5C9 can only be <4>

R4C4 can only be <3>

R4C2 can only be <8>

R2C9 is the only square in row 2 that can be <8>

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

R1C8=<17>

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

R1C8 - removing <17> from <157> leaving <5>

R1C2 can only be <1>

R1C9 can only be <6>

R2C8 can only be <7>

R8C8 can only be <4>

R1C1 can only be <7>

R9C9 can only be <3>

R3C7 can only be <1>

R2C1 can only be <9>

R3C3 can only be <2>

R8C7 can only be <9>

R8C1 can only be <3>

R7C7 can only be <6>

R8C2 can only be <2>

R9C8 can only be <1>

R9C2 can only be <4>

R9C1 can only be <6>

R8C9 can only be <5>

R2C2 can only be <5>

R3C2 can only be <6>

R8C3 can only be <1>

R7C2 can only be <9>



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