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Daily Sudoku Answer 



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Jul 22 - Very Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R3C9 can only be <6>

R3C8 is the only square in row 3 that can be <5>

R2C6 is the only square in column 6 that can be <6>

Intersection of row 3 with block 2. The value <1> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.

R1C5 - removing <1> from <149> leaving <49>

Squares R2C3<489>, R3C1<49> and R3C2<489> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <489>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C2 - removing <49> from <4679> leaving <67>

R1C3 - removing <49> from <4679> leaving <67>

Squares R8C4<15>, R8C5<135> and R8C6<13> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <135>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R8C3 - removing <1> from <167> leaving <67>

R8C7 - removing <1> from <167> leaving <67>

Squares R1C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R9C3 - removing <6> from <146> leaving <14>

Intersection of row 8 with block 8. The values <135> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.

R7C4 - removing <1> from <128> leaving <28>

R7C6 - removing <1> from <124> leaving <24>

R9C5 - removing <1> from <1248> leaving <248>

Squares R5C6 and R7C6 in column 6 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 5 and 7 can be removed.

R5C3 - removing <2> from <12489> leaving <1489>

R5C4 - removing <2> from <1259> leaving <159>

R7C4 - removing <2> from <28> leaving <8>

R5C5 - removing <2> from <12359> leaving <1359>

R5C8 - removing <2> from <23468> leaving <3468>

R7C8 - removing <2> from <128> leaving <18>

R7C8 can only be <1>

R1C8 can only be <4>

R1C5 can only be <9>

R2C7 can only be <9>

R2C4 can only be <2>

R1C7 can only be <1>

R3C4 can only be <1>

R3C6 can only be <4>

R8C4 can only be <5>

R3C1 can only be <9>

R7C6 can only be <2>

R2C5 can only be <8>

R7C9 can only be <7>

R9C5 can only be <4>

R5C9 can only be <2>

R8C7 can only be <6>

R5C4 can only be <9>

R8C3 can only be <7>

R9C7 can only be <8>

R9C2 can only be <6>

R9C3 can only be <1>

R9C8 can only be <2>

R6C7 can only be <5>

R4C8 can only be <3>

R2C3 can only be <4>

R3C2 can only be <8>

R7C1 can only be <4>

R6C8 can only be <8>

R4C7 can only be <4>

R5C8 can only be <6>

R7C2 can only be <9>

R5C1 can only be <1>

R6C2 can only be <3>

R1C3 can only be <6>

R1C2 can only be <7>

R4C3 can only be <2>

R5C3 can only be <8>

R6C3 can only be <9>

R4C2 can only be <5>

R5C7 can only be <7>

R5C6 can only be <3>

R5C5 can only be <5>

R8C6 can only be <1>

R6C5 can only be <2>

R8C5 can only be <3>

R4C5 can only be <1>

R5C2 can only be <4>



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