Jan 15 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <3>
R5C5 can only be <3>
R6C9 can only be <3>
R2C7 can only be <4>
R1C5 can only be <9>
R2C5 can only be <6>
R6C1 is the only square in row 6 that can be <4>
R7C4 is the only square in row 7 that can be <9>
R9C3 is the only square in column 3 that can be <8>
R3C9 is the only square in column 9 that can be <7>
R1C4 is the only square in column 4 that can be <7>
Squares R3C2<13>, R7C2<136> and R8C2<136> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <136>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C2 - removing <16> from <1679> leaving <79>
Intersection of column 2 with block 7. The value <6> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <6> from <1236> leaving <123>
Squares R2C2, R2C3, R5C2 and R5C3 form a Type-1 Unique Rectangle on <79>.
R5C3 - removing <79> from <1579> leaving <15>
R5C2 is the only square in row 5 that can be <7>
R2C2 can only be <9>
R2C3 can only be <7>
R5C9 is the only square in row 5 that can be <9>
R4C9 can only be <2>
R4C7 can only be <6>
R7C9 can only be <8>
R4C1 can only be <3>
R4C3 can only be <9>
R5C1 is the only square in row 5 that can be <6>
R9C6 is the only square in row 9 that can be <6>
Squares R5C3 and R6C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C3 - removing <1> from <123> leaving <23>
Squares R6C3, R6C7, R5C3 and R5C7 form a Type-1 Unique Rectangle on <15>.
R5C7 - removing <15> from <158> leaving <8>
R5C8 can only be <5>
R1C7 can only be <2>
R5C3 can only be <1>
R6C7 can only be <1>
R6C3 can only be <5>
R1C3 can only be <3>
R9C7 can only be <3>
R3C8 can only be <8>
R9C4 can only be <4>
R8C7 can only be <5>
R1C6 can only be <8>
R8C3 can only be <2>
R3C2 can only be <1>
R3C1 can only be <2>
R8C8 can only be <6>
R7C1 can only be <1>
R8C5 can only be <1>
R8C2 can only be <3>
R7C8 can only be <2>
R9C5 can only be <2>
R3C4 can only be <3>
R3C6 can only be <5>
R3C5 can only be <4>
R7C6 can only be <3>
R7C5 can only be <5>
R7C2 can only be <6>
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