Aug 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 can only be <3>
R6C9 can only be <2>
R5C6 can only be <2>
R9C4 can only be <7>
R5C5 can only be <9>
R4C5 can only be <4>
R6C1 can only be <9>
R4C9 can only be <5>
R9C6 can only be <3>
R1C4 can only be <5>
R1C6 can only be <7>
R8C5 can only be <2>
R2C5 can only be <3>
R4C1 can only be <2>
R5C8 can only be <8>
R5C2 can only be <5>
R6C5 can only be <7>
R1C2 is the only square in row 1 that can be <4>
R8C3 is the only square in row 8 that can be <4>
R9C9 is the only square in row 9 that can be <8>
R2C2 is the only square in column 2 that can be <9>
Intersection of column 2 with block 7. The values <67> 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 these values.
R9C1 - removing <6> from <16> leaving <1>
Intersection of column 9 with block 3. The value <6> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <6> from <369> leaving <39>
R2C8 - removing <6> from <156> leaving <15>
Squares R7C7<57>, R8C7<157>, R8C8<159> and R8C9<79> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1579>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <5> from <256> leaving <26>
Squares R9C2, R9C8, R7C2 and R7C8 form a Type-1 Unique Rectangle on <26>.
R7C2 - removing <26> from <267> leaving <7>
R7C7 can only be <5>
R8C2 can only be <3>
R7C3 can only be <2>
R3C7 can only be <8>
R8C1 can only be <5>
R3C2 can only be <2>
R9C2 can only be <6>
R3C3 can only be <5>
R7C8 can only be <6>
R9C8 can only be <2>
R2C1 can only be <6>
R2C9 can only be <7>
R1C1 can only be <3>
R2C7 can only be <1>
R8C9 can only be <9>
R3C8 can only be <3>
R2C3 can only be <8>
R1C8 can only be <9>
R8C8 can only be <1>
R1C9 can only be <6>
R2C8 can only be <5>
R8C7 can only be <7>
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