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Daily Sudoku Answer 



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Apr 30 - Super Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R5C5 can only be <1>

R5C7 can only be <7>

R8C6 can only be <4>

R5C4 can only be <5>

R4C5 can only be <4>

R9C6 can only be <1>

R2C6 can only be <7>

R1C6 can only be <5>

R6C5 can only be <9>

R5C6 can only be <6>

R5C3 can only be <3>

R3C7 is the only square in row 3 that can be <2>

R4C1 is the only square in row 4 that can be <1>

R4C2 is the only square in row 4 that can be <7>

R1C2 can only be <6>

R6C2 can only be <5>

R6C1 can only be <6>

R9C2 can only be <4>

R3C9 is the only square in row 3 that can be <6>

R4C9 can only be <8>

R4C8 can only be <6>

R9C1 is the only square in row 9 that can be <2>

R9C3 is the only square in row 9 that can be <6>

R9C9 is the only square in row 9 that can be <5>

Intersection of block 3 with row 1. The values <48> only appears in one or more of squares R1C7, R1C8 and R1C9 of block 3. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain these values.

R1C1 - removing <8> from <3789> leaving <379>

R1C3 - removing <8> from <78> leaving <7>

R1C4 - removing <8> from <138> leaving <13>

Squares R2C1 and R2C4 in row 2 and R8C1 and R8C4 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 4 can be removed.

R3C1 - removing <8> from <358> leaving <35>

R7C1 - removing <8> from <578> leaving <57>

R9C4 - removing <8> from <389> leaving <39>

Intersection of row 9 with block 9. The value <8> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R7C7 - removing <8> from <48> leaving <4>

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

R1C9=<14>

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

R1C9 - removing <14> from <149> leaving <9>

R1C1 can only be <3>

R1C7 can only be <8>

R2C9 can only be <1>

R8C9 can only be <7>

R2C4 can only be <8>

R8C1 can only be <8>

R7C9 can only be <3>

R1C4 can only be <1>

R3C1 can only be <5>

R1C8 can only be <4>

R9C7 can only be <9>

R6C8 can only be <3>

R2C1 can only be <9>

R8C4 can only be <9>

R3C5 can only be <3>

R3C3 can only be <8>

R7C1 can only be <7>

R7C3 can only be <5>

R7C5 can only be <8>

R6C9 can only be <4>

R9C8 can only be <8>

R9C4 can only be <3>



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