Jun 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <3>
R9C9 can only be <5>
R8C7 can only be <2>
R8C5 can only be <8>
R8C2 can only be <5>
R8C3 can only be <9>
R1C9 is the only square in row 1 that can be <1>
R1C6 is the only square in row 1 that can be <6>
R3C3 is the only square in row 3 that can be <3>
R3C7 is the only square in row 3 that can be <5>
R4C4 is the only square in row 4 that can be <5>
R7C6 is the only square in row 7 that can be <3>
R4C5 is the only square in row 4 that can be <3>
R7C4 is the only square in row 7 that can be <1>
R9C1 is the only square in row 9 that can be <3>
R5C8 is the only square in column 8 that can be <8>
R5C5 is the only square in row 5 that can be <6>
Squares R4C9 and R6C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C7 - removing <67> from <1467> leaving <14>
R6C7 - removing <67> from <1467> leaving <14>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <4> from <467> leaving <67>
Intersection of column 1 with block 4. The value <7> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C2 - removing <7> from <127> leaving <12>
R5C4 is the only square in row 5 that can be <7>
Squares R7C7, R7C8, R2C7 and R2C8 form a Type-1 Unique Rectangle on <67>.
R2C8 - removing <67> from <467> leaving <4>
R2C5 can only be <2>
R3C8 can only be <7>
R3C2 can only be <8>
R7C8 can only be <6>
R2C7 can only be <6>
R7C7 can only be <7>
R2C3 can only be <1>
R6C5 can only be <4>
R1C4 can only be <8>
R7C2 can only be <2>
R1C1 can only be <2>
R6C7 can only be <1>
R4C7 can only be <4>
R7C3 can only be <8>
R5C2 can only be <1>
R2C2 can only be <7>
R4C3 can only be <6>
R4C9 can only be <7>
R6C3 can only be <2>
R4C1 can only be <8>
R6C9 can only be <6>
R5C6 can only be <2>
R9C6 can only be <4>
R6C4 can only be <9>
R6C6 can only be <8>
R3C4 can only be <4>
R6C1 can only be <7>
R4C6 can only be <1>
R9C4 can only be <2>
R3C6 can only be <9>
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