Oct 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <7>
R7C2 can only be <5>
R8C3 can only be <8>
R6C2 can only be <3>
R7C3 can only be <7>
R9C1 can only be <1>
R2C4 is the only square in row 2 that can be <1>
R8C4 can only be <4>
R8C6 can only be <3>
R8C7 can only be <1>
R7C6 can only be <2>
R1C5 is the only square in row 1 that can be <3>
R3C6 is the only square in row 3 that can be <4>
R4C3 is the only square in row 4 that can be <4>
R6C8 is the only square in row 6 that can be <1>
R7C5 is the only square in row 7 that can be <1>
R3C8 is the only square in column 8 that can be <2>
R1C1 is the only square in row 1 that can be <2>
R5C1 can only be <5>
R6C3 can only be <2>
R5C9 is the only square in row 5 that can be <2>
R6C7 is the only square in row 6 that can be <5>
R3C3 is the only square in column 3 that can be <5>
Squares R9C5 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <68> from <5678> leaving <57>
Intersection of column 9 with block 6. The value <7> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <7> from <36789> leaving <3689>
Squares R2C7<679>, R3C7<679> and R5C7<69> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C7 - removing <69> from <3689> leaving <38>
R7C7 - removing <6> from <368> leaving <38>
Squares R2C3 and R2C7 in row 2 and R5C3 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C7 - removing <6> from <679> leaving <79>
Squares R3C2 and R5C7 form a remote naked pair. <69> can be removed from any square that is common to their groups.
R3C7 - removing <9> from <79> leaving <7>
R2C6 is the only square in row 2 that can be <7>
R9C6 can only be <5>
R9C4 can only be <7>
R1C6 can only be <9>
R1C9 can only be <6>
R1C4 can only be <5>
R9C9 can only be <8>
R2C7 can only be <9>
R2C3 can only be <6>
R5C7 can only be <6>
R5C3 can only be <9>
R4C8 can only be <3>
R9C5 can only be <6>
R6C9 can only be <7>
R7C7 can only be <3>
R3C2 can only be <9>
R4C2 can only be <6>
R4C7 can only be <8>
R7C8 can only be <6>
R6C1 can only be <8>
R4C9 can only be <9>
R7C4 can only be <8>
R3C5 can only be <8>
R3C4 can only be <6>
R4C1 can only be <7>
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