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Daily Sudoku Answer 



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Nov 19 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s141841



Reasoning 



R4C5 is the only square in row 4 that can be <9>

R2C5 can only be <1>

R6C5 can only be <7>

R8C5 can only be <8>

R8C6 is the only square in row 8 that can be <7>

R8C8 is the only square in row 8 that can be <9>

R2C4 is the only square in column 4 that can be <3>

R2C2 is the only square in row 2 that can be <9>

R1C4 is the only square in row 1 that can be <9>

R2C3 is the only square in row 2 that can be <6>

R2C1 is the only square in row 2 that can be <7>

R8C2 is the only square in row 8 that can be <6>

R8C7 is the only square in row 8 that can be <5>

R2C7 can only be <4>

R9C2 is the only square in row 9 that can be <5>

R9C8 is the only square in row 9 that can be <6>

R1C2 is the only square in column 2 that can be <8>

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

R5C4 can only be <1>

R9C4 can only be <2>

R9C6 can only be <1>

R8C4 can only be <4>

Squares R3C2 and R3C3 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R3C8 - removing <2> from <123> leaving <13>

Intersection of column 1 with block 4. The value <4> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. 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 <4> from <1347> leaving <137>

R6C2 - removing <4> from <124> leaving <12>

Intersection of column 3 with block 7. The value <1> 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.

R7C2 - removing <1> from <1234> leaving <234>

Squares R4C1 and R8C1 in column 1 and R4C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 4 and 8 can be removed.

R4C2 - removing <3> from <137> leaving <17>

R4C8 - removing <3> from <1347> leaving <147>

Squares R1C6, R1C8, R2C6 and R2C8 form a Type-1 Unique Rectangle on <25>.

R2C8 - removing <25> from <258> leaving <8>

R2C9 can only be <2>

R2C6 can only be <5>

R1C8 can only be <5>

R1C6 can only be <2>

R6C9 is the only square in row 6 that can be <8>

R7C8 is the only square in column 8 that can be <2>

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

R4C8=<47>

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

R4C8 - removing <47> from <147> leaving <1>

R4C2 can only be <7>

R4C9 can only be <3>

R3C8 can only be <3>

R6C8 can only be <4>

R4C1 can only be <4>

R8C9 can only be <1>

R5C8 can only be <7>

R5C2 can only be <3>

R6C1 can only be <2>

R8C3 can only be <2>

R7C7 can only be <3>

R3C7 can only be <1>

R7C2 can only be <4>

R6C2 can only be <1>

R8C1 can only be <3>

R7C3 can only be <1>

R3C2 can only be <2>

R3C3 can only be <4>



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