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Daily Sudoku Answer 



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Dec 03 - Super Hard
Puzzle Copyright © Kevin Stone

Share link – www.brainbashers.com/s193794



Reasoning 



R4C4 can only be <8>

R5C2 can only be <7>

R5C4 can only be <4>

R6C3 can only be <8>

R3C4 can only be <7>

R6C6 can only be <7>

R6C7 can only be <4>

R6C5 can only be <5>

R7C4 can only be <5>

R2C5 can only be <8>

R6C4 can only be <1>

R3C5 can only be <2>

R3C6 can only be <4>

R1C1 is the only square in row 1 that can be <4>

R7C9 is the only square in row 7 that can be <4>

R3C1 is the only square in column 1 that can be <8>

R7C6 is the only square in column 6 that can be <8>

R9C8 is the only square in column 8 that can be <9>

R7C1 is the only square in column 1 that can be <9>

R8C1 is the only square in column 1 that can be <2>

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

R1C9 is the only square in row 1 that can be <2>

R9C9 is the only square in column 9 that can be <8>

Squares R7C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R4C5 - removing <3> from <369> leaving <69>

R5C5 - removing <3> from <369> leaving <69>

Intersection of column 9 with block 3. The value <6> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R3C7 - removing <6> from <356> leaving <35>

Squares R1C8, R5C8, R1C7 and R5C7 form a Type-4 Unique Rectangle on <38>.

R1C7 - removing <3> from <3578> leaving <578>

R5C7 - removing <3> from <368> leaving <68>

Squares R1C3 (XYZ), R1C2 (XZ) and R7C3 (YZ) form an XYZ-Wing pattern on <3>. All squares that are buddies of all three squares cannot be <3>.

R3C3 - removing <3> from <356> leaving <56>

Intersection of row 3 with block 3. The value <3> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R1C8 - removing <3> from <38> leaving <8>

R5C8 can only be <3>

R5C6 can only be <2>

R4C7 can only be <6>

R4C5 can only be <9>

R5C7 can only be <8>

R5C3 can only be <9>

R4C6 can only be <3>

R4C3 can only be <2>

R5C5 can only be <6>

Squares R1C7 (XY), R1C2 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.

R9C2 - removing <3> from <35> leaving <5>

R1C2 can only be <3>

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

R9C3=<36>

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

R9C3 - removing <36> from <367> leaving <7>

R9C1 can only be <6>

R9C7 can only be <3>

R1C3 can only be <5>

R7C3 can only be <3>

R3C7 can only be <5>

R8C9 can only be <7>

R1C7 can only be <7>

R3C3 can only be <6>

R2C9 can only be <6>

R2C1 can only be <7>

R3C9 can only be <3>

R7C5 can only be <7>

R8C5 can only be <3>



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