Sep 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <3>
R9C4 can only be <4>
R2C8 is the only square in row 2 that can be <7>
R4C8 is the only square in row 4 that can be <2>
R3C2 is the only square in row 3 that can be <2>
R2C7 is the only square in column 7 that can be <2>
Squares R2C1<145>, R2C2<145> and R2C4<15> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C5 - removing <145> from <145689> leaving <689>
R2C6 - removing <5> from <5689> leaving <689>
R2C9 - removing <4> from <489> leaving <89>
Intersection of row 2 with block 1. The value <4> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <4> from <145> leaving <15>
Intersection of block 3 with column 8. The value <4> only appears in one or more of squares R1C8, R2C8 and R3C8 of block 3. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R5C8 - removing <4> from <145689> leaving <15689>
R6C8 - removing <4> from <14569> leaving <1569>
R8C8 - removing <4> from <34569> leaving <3569>
Squares R5C3 and R8C3 in column 3 and R5C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C2 - removing <9> from <3456789> leaving <345678>
R8C2 - removing <9> from <13689> leaving <1368>
R5C6 - removing <9> from <59> leaving <5>
R5C8 - removing <9> from <15689> leaving <1568>
R8C8 - removing <9> from <3569> leaving <356>
R5C9 - removing <9> from <45689> leaving <4568>
R8C9 - removing <9> from <4569> leaving <456>
R2C6 is the only square in column 6 that can be <9>
R2C9 can only be <8>
R3C5 can only be <4>
R2C5 can only be <6>
R1C8 can only be <4>
R3C8 can only be <9>
R9C2 is the only square in row 9 that can be <9>
R8C3 can only be <6>
R5C3 can only be <9>
R7C2 can only be <3>
R5C7 can only be <4>
R5C9 can only be <6>
R8C7 can only be <9>
R7C5 can only be <5>
R7C8 can only be <6>
R9C8 can only be <3>
R9C5 can only be <8>
R8C8 can only be <5>
R8C9 can only be <4>
R6C8 can only be <1>
R9C6 can only be <6>
R1C5 can only be <1>
R8C6 can only be <2>
R1C2 can only be <5>
R6C5 can only be <9>
R2C4 can only be <5>
R1C4 can only be <2>
R6C9 can only be <5>
R4C5 can only be <7>
R5C8 can only be <8>
R6C1 can only be <4>
R4C9 can only be <9>
R8C4 can only be <7>
R1C6 can only be <8>
R4C2 can only be <8>
R8C5 can only be <3>
R5C4 can only be <1>
R5C1 can only be <3>
R5C2 can only be <7>
R6C2 can only be <6>
R2C1 can only be <1>
R2C2 can only be <4>
R8C1 can only be <8>
R4C1 can only be <5>
R8C2 can only be <1>
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