Jul 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 can only be <8>
R3C3 can only be <4>
R3C4 can only be <5>
R1C1 can only be <2>
R3C6 can only be <9>
R3C9 can only be <6>
R2C1 can only be <7>
R2C3 can only be <3>
R7C1 can only be <6>
R2C2 can only be <9>
R4C1 can only be <5>
R1C5 is the only square in row 1 that can be <4>
R4C2 is the only square in row 4 that can be <4>
R5C4 is the only square in row 5 that can be <3>
R5C7 is the only square in row 5 that can be <4>
R6C2 is the only square in row 6 that can be <8>
R6C6 is the only square in row 6 that can be <7>
R7C4 is the only square in row 7 that can be <7>
R7C7 is the only square in row 7 that can be <8>
R8C2 is the only square in row 8 that can be <3>
R8C5 is the only square in row 8 that can be <6>
R6C8 is the only square in row 6 that can be <6>
R4C3 is the only square in row 4 that can be <6>
R5C6 is the only square in row 5 that can be <6>
R9C6 is the only square in column 6 that can be <5>
R8C8 is the only square in column 8 that can be <7>
Squares R5C2 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <2> from <125> leaving <15>
Squares R8C3 and R8C4 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C7 - removing <2> from <259> leaving <59>
R8C9 - removing <2> from <259> leaving <59>
R6C7 is the only square in column 7 that can be <2>
Intersection of column 7 with block 3. The value <1> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. 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 <1> from <189> leaving <89>
R2C8 - removing <1> from <158> leaving <58>
Squares R5C2, R5C3, R9C2 and R9C3 form a Type-1 Unique Rectangle on <27>.
R9C3 - removing <27> from <278> leaving <8>
R8C3 can only be <2>
R8C4 can only be <8>
R5C3 can only be <7>
R9C2 can only be <7>
R1C4 can only be <1>
R5C2 can only be <2>
R1C7 can only be <9>
R4C4 can only be <2>
R2C6 can only be <2>
R1C8 can only be <8>
R8C7 can only be <5>
R2C8 can only be <5>
R2C5 can only be <8>
R7C6 can only be <1>
R2C7 can only be <1>
R5C8 can only be <1>
R5C5 can only be <5>
R4C8 can only be <9>
R7C9 can only be <2>
R9C5 can only be <2>
R9C9 can only be <1>
R8C9 can only be <9>
R6C9 can only be <5>
R4C5 can only be <1>
R6C5 can only be <9>
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