Aug 04 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <2>
R9C4 can only be <2>
R1C4 can only be <7>
R1C6 can only be <9>
R1C7 is the only square in row 1 that can be <3>
R2C3 is the only square in row 2 that can be <8>
R3C3 is the only square in row 3 that can be <9>
R4C4 is the only square in row 4 that can be <5>
R4C5 is the only square in row 4 that can be <9>
R5C6 is the only square in row 5 that can be <2>
R5C4 is the only square in row 5 that can be <8>
R6C4 can only be <3>
R5C8 is the only square in row 5 that can be <3>
R6C5 is the only square in row 6 that can be <1>
R6C6 is the only square in row 6 that can be <7>
R8C7 is the only square in row 8 that can be <8>
R9C3 is the only square in row 9 that can be <3>
R7C3 is the only square in column 3 that can be <1>
Squares R8C3 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <46> from <2467> leaving <27>
R8C8 - removing <46> from <2467> leaving <27>
Squares R4C9 and R6C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <4> from <246> leaving <26>
R3C9 - removing <4> from <1245> leaving <125>
R7C9 - removing <4> from <2456> leaving <256>
R9C9 - removing <4> from <1456> leaving <156>
Intersection of row 1 with block 1. The value <4> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <4> from <2457> leaving <257>
R3C2 - removing <4> from <2457> leaving <257>
Squares R5C2 and R8C3 form a remote naked pair. <46> can be removed from any square that is common to their groups.
R7C2 - removing <46> from <24567> leaving <257>
R5C2 is the only square in column 2 that can be <4>
R5C5 can only be <6>
R6C1 can only be <8>
R8C5 can only be <4>
R4C6 can only be <4>
R6C9 can only be <4>
R4C1 can only be <6>
R4C9 can only be <8>
R8C3 can only be <6>
R9C6 can only be <6>
R1C3 can only be <4>
R1C1 can only be <2>
R1C9 can only be <6>
R2C8 can only be <7>
R2C7 can only be <5>
R8C8 can only be <2>
R8C2 can only be <7>
R3C8 can only be <4>
R7C9 can only be <5>
R2C2 can only be <6>
R3C7 can only be <1>
R7C8 can only be <6>
R9C9 can only be <1>
R3C2 can only be <5>
R7C2 can only be <2>
R7C1 can only be <4>
R9C7 can only be <4>
R3C9 can only be <2>
R3C1 can only be <7>
R7C7 can only be <7>
R9C1 can only be <5>
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