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Daily Sudoku Answer 



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Mar 26 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s187817



Reasoning 



R4C5 can only be <4>

R5C4 can only be <1>

R5C6 can only be <3>

R6C1 can only be <6>

R9C6 can only be <5>

R5C5 can only be <8>

R6C5 can only be <5>

R6C9 can only be <8>

R2C5 can only be <2>

R9C4 can only be <2>

R1C6 can only be <9>

R3C5 can only be <7>

R7C5 can only be <1>

R1C4 can only be <5>

R8C5 can only be <6>

R1C3 is the only square in row 1 that can be <6>

R2C9 is the only square in row 2 that can be <3>

R5C7 is the only square in row 5 that can be <6>

R9C1 is the only square in row 9 that can be <3>

R9C9 is the only square in row 9 that can be <6>

R3C7 is the only square in column 7 that can be <5>

Intersection of column 3 with block 7. The value <8> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.

R7C1 - removing <8> from <489> leaving <49>

Squares R3C1 and R3C9 in row 3 and R4C1 and R4C9 in row 4 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 9 can be removed.

R1C1 - removing <2> from <1248> leaving <148>

R1C9 - removing <2> from <1247> leaving <147>

R7C9 - removing <2> from <249> leaving <49>

R7C7 is the only square in row 7 that can be <2>

R7C3 is the only square in row 7 that can be <8>

Squares R4C1 and R4C9 in row 4 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.

R3C1 - removing <9> from <129> leaving <12>

R8C1 - removing <9> from <159> leaving <15>

R8C9 - removing <9> from <179> leaving <17>

R3C3 is the only square in row 3 that can be <9>

R5C3 can only be <4>

R9C3 can only be <1>

R8C1 can only be <5>

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

Squares R2C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C8 - removing <48> from <1248> leaving <12>

Squares R1C8 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C9 - removing <1> from <147> leaving <47>

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

R1C1=<18>

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

R1C1 - removing <18> from <148> leaving <4>

R1C2 can only be <2>

R1C9 can only be <7>

R2C1 can only be <8>

R7C1 can only be <9>

R1C8 can only be <1>

R5C2 can only be <9>

R3C1 can only be <1>

R8C8 can only be <9>

R3C9 can only be <2>

R1C7 can only be <8>

R8C9 can only be <1>

R2C8 can only be <4>

R9C8 can only be <8>

R4C9 can only be <9>

R4C1 can only be <2>

R7C9 can only be <4>

R5C8 can only be <2>

R8C2 can only be <7>

R9C2 can only be <4>

R9C7 can only be <7>



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