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Daily Sudoku Answer 



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Dec 18 - Very Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R4C4 can only be <6>

R5C8 can only be <7>

R7C5 can only be <6>

R5C7 can only be <6>

R4C9 can only be <5>

R6C9 can only be <8>

R5C4 is the only square in row 5 that can be <8>

R9C4 can only be <4>

R9C6 can only be <9>

R6C4 can only be <3>

R6C6 can only be <4>

R8C5 can only be <8>

R6C5 can only be <9>

R1C4 can only be <5>

R6C1 can only be <5>

R1C3 is the only square in column 3 that can be <9>

R3C5 is the only square in column 5 that can be <3>

Squares R2C1<47>, R2C2<45>, R3C1<147> and R3C3<145> in block 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1457>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C1 - removing <17> from <1678> leaving <68>

R1C2 - removing <1> from <168> leaving <68>

Intersection of row 1 with block 3. The values <13> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.

R3C7 - removing <1> from <157> leaving <57>

R3C9 - removing <1> from <147> leaving <47>

Squares R2C1<47>, R3C1<147>, R4C1<12> and R7C1<124> in column 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1247>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R8C1 - removing <1> from <136> leaving <36>

R9C1 - removing <2> from <2368> leaving <368>

Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.

R9C3 - removing <5> from <25> leaving <2>

R9C7 - removing <5> from <357> leaving <37>

R5C6 is the only square in row 5 that can be <2>

R1C6 can only be <7>

R4C5 can only be <7>

R4C6 can only be <1>

R2C5 can only be <2>

R4C1 can only be <2>

R7C9 is the only square in row 7 that can be <2>

R1C9 can only be <1>

R1C7 can only be <3>

R1C8 can only be <2>

R9C7 can only be <7>

R9C9 can only be <6>

R3C7 can only be <5>

R8C9 can only be <9>

R7C7 can only be <1>

R2C8 can only be <9>

R7C1 can only be <4>

R8C8 can only be <3>

R7C3 can only be <5>

R2C1 can only be <7>

R9C2 can only be <8>

R8C1 can only be <6>

R9C8 can only be <5>

R9C1 can only be <3>

R1C2 can only be <6>

R1C1 can only be <8>

R8C2 can only be <1>

R2C9 can only be <4>

R3C1 can only be <1>

R2C2 can only be <5>

R3C9 can only be <7>

R3C3 can only be <4>

R5C3 can only be <1>

R5C2 can only be <4>



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