Jan 25 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <8>
R5C4 can only be <8>
R5C6 can only be <3>
R6C6 can only be <4>
R4C4 can only be <7>
R2C8 is the only square in row 2 that can be <8>
R8C8 can only be <9>
R3C8 can only be <6>
R9C8 can only be <2>
R4C8 can only be <5>
R8C5 is the only square in row 8 that can be <8>
R8C6 is the only square in row 8 that can be <7>
R1C1 is the only square in column 1 that can be <6>
R9C3 is the only square in column 3 that can be <7>
R6C3 is the only square in column 3 that can be <8>
Intersection of row 2 with block 2. The values <69> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C4 - removing <9> from <1249> leaving <124>
R1C5 - removing <9> from <4579> leaving <457>
R3C4 - removing <9> from <1249> leaving <124>
R3C5 - removing <9> from <3479> leaving <347>
Squares R5C7<169>, R5C9<169> and R6C7<19> in block 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <169>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C9 - removing <19> from <1239> leaving <23>
Squares R1C4<124>, R3C4<124> and R3C6<12> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C5 - removing <4> from <457> leaving <57>
R3C5 - removing <4> from <347> leaving <37>
Intersection of column 5 with block 8. The value <4> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <4> from <2469> leaving <269>
R8C4 - removing <4> from <14> leaving <1>
R8C2 can only be <4>
R7C2 can only be <5>
R7C1 can only be <8>
R1C2 can only be <2>
R2C2 can only be <3>
R1C4 can only be <4>
R3C4 can only be <2>
R6C2 can only be <1>
R3C6 can only be <1>
R6C7 can only be <9>
R6C1 can only be <3>
R9C1 can only be <1>
R6C9 can only be <2>
R4C1 can only be <4>
R4C9 can only be <3>
R4C3 can only be <2>
R3C1 can only be <9>
R3C3 can only be <4>
R3C9 can only be <7>
R5C1 can only be <5>
R1C3 can only be <5>
R3C5 can only be <3>
R7C9 can only be <6>
R1C7 can only be <1>
R5C3 can only be <9>
R7C4 can only be <9>
R7C6 can only be <2>
R5C9 can only be <1>
R9C9 can only be <8>
R9C7 can only be <4>
R9C5 can only be <5>
R7C7 can only be <7>
R1C5 can only be <7>
R1C9 can only be <9>
R5C7 can only be <6>
R7C5 can only be <4>
R2C4 can only be <6>
R9C6 can only be <6>
R2C5 can only be <9>
R2C6 can only be <5>
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