Jul 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C2 can only be <9>
R5C4 can only be <1>
R6C5 can only be <3>
R6C8 can only be <4>
R4C8 can only be <5>
R5C1 can only be <4>
R4C5 can only be <7>
R5C9 can only be <9>
R6C2 can only be <8>
R2C1 is the only square in row 2 that can be <3>
R8C7 is the only square in row 8 that can be <3>
R8C9 is the only square in row 8 that can be <5>
Intersection of column 7 with block 3. The value <9> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. 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 <9> from <1679> leaving <167>
R3C8 - removing <9> from <1679> leaving <167>
Intersection of block 2 with row 2. The value <7> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.
R2C2 - removing <7> from <2467> leaving <246>
R2C8 - removing <7> from <167> leaving <16>
R2C9 - removing <7> from <12478> leaving <1248>
Intersection of block 8 with row 8. The value <7> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C1 - removing <7> from <12789> leaving <1289>
R8C2 - removing <7> from <2467> leaving <246>
R8C8 - removing <7> from <179> leaving <19>
Squares R9C3<46>, R9C5<468> and R9C7<48> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <8> from <178> leaving <17>
R9C9 - removing <48> from <1478> leaving <17>
Squares R7C8<79>, R8C8<19> and R9C9<17> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <179>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <7> from <478> leaving <48>
Squares R1C3<459>, R1C5<459> and R1C7<49> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <459>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <9> from <279> leaving <27>
R1C9 - removing <4> from <247> leaving <27>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C1 - removing <7> from <79> leaving <9>
R3C9 - removing <7> from <147> leaving <14>
R7C1 - removing <7> from <2789> leaving <289>
R7C8 is the only square in row 7 that can be <9>
R8C8 can only be <1>
R2C8 can only be <6>
R9C9 can only be <7>
R9C1 can only be <1>
R1C9 can only be <2>
R1C1 can only be <7>
R3C8 can only be <7>
R2C2 is the only square in row 2 that can be <2>
R3C2 is the only square in row 3 that can be <6>
R8C2 can only be <4>
R8C4 can only be <7>
R7C2 can only be <7>
R9C3 can only be <6>
R8C6 can only be <6>
R2C4 can only be <4>
R8C3 can only be <9>
R5C6 can only be <5>
R2C3 can only be <5>
R3C5 can only be <1>
R3C9 can only be <4>
R7C9 can only be <8>
R1C7 can only be <9>
R5C5 can only be <6>
R2C6 can only be <7>
R7C1 can only be <2>
R2C9 can only be <1>
R9C7 can only be <4>
R9C5 can only be <8>
R1C5 can only be <5>
R2C7 can only be <8>
R2C5 can only be <9>
R1C3 can only be <4>
R7C5 can only be <4>
R8C1 can only be <8>
R8C5 can only be <2>
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