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Daily Sudoku Answer 



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Oct 29 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s202116



Reasoning 



R1C7 can only be <5>

R4C6 is the only square in row 4 that can be <8>

R1C3 is the only square in column 3 that can be <8>

Squares R4C1 and R5C3 in block 4 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 block.

R5C2 - removing <4> from <469> leaving <69>

R6C1 - removing <14> from <1469> leaving <69>

Squares R1C8<46>, R1C9<469> and R3C9<49> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R2C8 - removing <4> from <148> leaving <18>

R2C9 - removing <49> from <1489> leaving <18>

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

R2C9 - removing <1> from <18> leaving <8>

R6C9 - removing <1> from <14> leaving <4>

R9C1 - removing <1> from <124567> leaving <24567>

R9C9 - removing <1> from <12356> leaving <2356>

R2C8 can only be <1>

R3C9 can only be <9>

R5C8 can only be <2>

R1C9 can only be <6>

R9C8 can only be <6>

R1C8 can only be <4>

R8C8 can only be <8>

R6C6 is the only square in row 6 that can be <1>

R5C6 is the only square in column 6 that can be <4>

R5C3 can only be <1>

R5C7 can only be <3>

R9C3 can only be <4>

R4C1 can only be <4>

R9C7 can only be <1>

R4C9 can only be <1>

R3C1 can only be <7>

R3C5 can only be <4>

R2C2 is the only square in row 2 that can be <4>

R7C1 is the only square in row 7 that can be <1>

R9C9 is the only square in row 9 that can be <3>

Squares R7C5, R7C9, R8C5 and R8C9 form a Type-1 Unique Rectangle on <25>.

R8C5 - removing <25> from <257> leaving <7>

R9C6 can only be <9>

R1C6 can only be <7>

R6C4 is the only square in row 6 that can be <7>

R9C2 is the only square in row 9 that can be <7>

Squares R2C1 and R2C5 in row 2 and R6C1 and R6C5 in row 6 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 5 can be removed.

R1C1 - removing <9> from <239> leaving <23>

R5C5 - removing <9> from <569> leaving <56>

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

R8C1=<56>

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

R8C1 - removing <56> from <256> leaving <2>

R8C2 can only be <6>

R8C9 can only be <5>

R1C1 can only be <3>

R9C1 can only be <5>

R5C2 can only be <9>

R7C9 can only be <2>

R9C4 can only be <2>

R4C4 can only be <3>

R7C5 can only be <5>

R1C4 can only be <9>

R2C1 can only be <9>

R1C2 can only be <2>

R5C4 can only be <5>

R2C5 can only be <3>

R6C1 can only be <6>

R4C5 can only be <2>

R5C5 can only be <6>

R6C5 can only be <9>



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