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Daily Sudoku Answer 



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Dec 17 - Very Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R5C9 can only be <6>

R7C3 can only be <5>

R5C3 can only be <3>

R8C3 can only be <2>

R8C9 can only be <9>

R2C3 can only be <6>

R3C3 can only be <1>

R2C9 can only be <2>

R1C8 is the only square in row 1 that can be <6>

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

R2C7 is the only square in row 2 that can be <9>

R4C5 is the only square in row 4 that can be <3>

R4C4 is the only square in row 4 that can be <9>

R4C2 is the only square in row 4 that can be <6>

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

R7C7 is the only square in row 7 that can be <6>

R9C8 is the only square in row 9 that can be <2>

R8C4 is the only square in column 4 that can be <1>

R5C6 is the only square in column 6 that can be <2>

Squares R7C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R8C2 - removing <8> from <378> leaving <37>

Squares R1C2 and R1C5 in row 1 and R6C2 and R6C5 in row 6 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 5 can be removed.

R3C2 - removing <5> from <235> leaving <23>

R3C5 - removing <5> from <257> leaving <27>

R5C5 - removing <5> from <4578> leaving <478>

Intersection of row 3 with block 3. The value <5> 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.

R2C8 - removing <5> from <357> leaving <37>

Squares R2C6 and R2C8 in row 2 and R4C6 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 6 and 8 can be removed.

R3C8 - removing <7> from <357> leaving <35>

R6C6 - removing <7> from <147> leaving <14>

R6C8 - removing <7> from <147> leaving <14>

Squares R6C6 and R6C8 in row 6 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 row.

R6C5 - removing <4> from <457> leaving <57>

Squares R1C5<25>, R3C5<27> and R6C5<57> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R5C5 - removing <7> from <478> leaving <48>

Squares R9C2, R9C5, R7C2 and R7C5 form a Type-1 Unique Rectangle on <89>.

R7C5 - removing <89> from <489> leaving <4>

R7C8 can only be <8>

R5C5 can only be <8>

R8C6 can only be <8>

R7C2 can only be <9>

R2C6 can only be <7>

R9C5 can only be <9>

R9C2 can only be <8>

R2C8 can only be <3>

R4C6 can only be <1>

R3C5 can only be <2>

R2C1 can only be <5>

R3C8 can only be <5>

R3C2 can only be <3>

R1C5 can only be <5>

R3C7 can only be <7>

R8C8 can only be <4>

R4C8 can only be <7>

R6C6 can only be <4>

R5C7 can only be <4>

R5C4 can only be <5>

R8C7 can only be <5>

R6C8 can only be <1>

R1C2 can only be <2>

R6C5 can only be <7>

R2C4 can only be <8>

R5C1 can only be <7>

R8C2 can only be <7>

R8C1 can only be <3>

R6C2 can only be <5>



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