Oct 04 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C3 can only be <6>
R5C5 can only be <5>
R3C5 is the only square in row 3 that can be <6>
R1C1 is the only square in row 1 that can be <6>
R5C2 is the only square in row 5 that can be <1>
R6C8 is the only square in row 6 that can be <5>
R6C6 is the only square in row 6 that can be <6>
R9C9 is the only square in row 9 that can be <6>
R4C2 is the only square in column 2 that can be <7>
R4C4 is the only square in column 4 that can be <4>
R8C7 is the only square in column 7 that can be <8>
R8C3 can only be <2>
R2C3 can only be <8>
R7C5 is the only square in row 7 that can be <2>
R4C8 is the only square in column 8 that can be <8>
Squares R4C9 and R6C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <9> from <1479> leaving <147>
R2C9 - removing <9> from <1479> leaving <147>
R8C9 - removing <3> from <347> leaving <47>
Intersection of row 2 with block 2. The values <39> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C4 - removing <9> from <1279> leaving <127>
R1C6 - removing <9> from <1279> leaving <127>
Squares R1C9<147>, R2C7<47> and R2C9<147> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <147>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <47> from <2479> leaving <29>
Squares R3C2, R3C8, R1C2 and R1C8 form a Type-1 Unique Rectangle on <29>.
R1C2 - removing <29> from <249> leaving <4>
R7C2 can only be <3>
R2C1 can only be <2>
R4C1 can only be <3>
R3C2 can only be <9>
R3C8 can only be <2>
R1C8 can only be <9>
R4C9 can only be <9>
R6C1 can only be <8>
R4C6 can only be <2>
R6C9 can only be <3>
R6C2 can only be <2>
R9C1 can only be <5>
R6C4 can only be <9>
R7C8 can only be <4>
R9C2 can only be <8>
R5C8 can only be <7>
R8C9 can only be <7>
R8C4 can only be <3>
R1C9 can only be <1>
R9C8 can only be <3>
R8C1 can only be <4>
R2C9 can only be <4>
R2C7 can only be <7>
R1C6 can only be <7>
R5C7 can only be <4>
R8C5 can only be <9>
R8C6 can only be <5>
R2C5 can only be <3>
R1C4 can only be <2>
R9C6 can only be <1>
R2C4 can only be <1>
R2C6 can only be <9>
R9C4 can only be <7>
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