Jun 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 is the only square in row 1 that can be <8>
R2C5 is the only square in row 2 that can be <9>
R8C5 can only be <8>
R2C3 is the only square in row 2 that can be <5>
R1C1 can only be <1>
R3C9 is the only square in row 3 that can be <1>
R5C5 is the only square in row 5 that can be <3>
R7C2 is the only square in row 7 that can be <1>
R9C2 is the only square in row 9 that can be <3>
R3C1 is the only square in row 3 that can be <3>
R7C8 is the only square in row 7 that can be <3>
R5C1 is the only square in column 1 that can be <5>
R9C4 is the only square in column 4 that can be <9>
R9C3 can only be <4>
R9C9 can only be <7>
R8C1 can only be <9>
R9C7 can only be <5>
R2C9 can only be <4>
R7C9 can only be <9>
R2C2 can only be <7>
R7C1 can only be <6>
R9C6 can only be <6>
R3C2 can only be <4>
R6C1 can only be <4>
R1C4 is the only square in row 1 that can be <6>
R5C6 is the only square in column 6 that can be <4>
Squares R3C5 and R7C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <5> from <156> leaving <16>
R6C5 - removing <7> from <167> leaving <16>
R4C4 is the only square in row 4 that can be <5>
Squares R4C9 and R5C9 in block 6 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 block.
R4C7 - removing <2> from <124> leaving <14>
R4C8 - removing <2> from <246> leaving <46>
R5C7 - removing <2> from <127> leaving <17>
R5C8 - removing <2> from <2679> leaving <679>
R6C8 - removing <2> from <2679> leaving <679>
Squares R4C5<16>, R4C7<14> and R4C8<46> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <146>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <6> from <268> leaving <28>
Squares R4C2, R4C9, R5C2 and R5C9 form a Type-1 Unique Rectangle on <28>.
R5C2 - removing <28> from <268> leaving <6>
R6C2 can only be <2>
R6C6 can only be <7>
R4C2 can only be <8>
R7C6 can only be <5>
R5C4 can only be <2>
R7C5 can only be <7>
R1C6 can only be <2>
R1C7 can only be <7>
R3C4 can only be <7>
R1C8 can only be <5>
R5C7 can only be <1>
R3C8 can only be <2>
R3C5 can only be <5>
R8C8 can only be <4>
R4C9 can only be <2>
R5C9 can only be <8>
R5C3 can only be <9>
R4C7 can only be <4>
R8C7 can only be <2>
R4C8 can only be <6>
R4C5 can only be <1>
R6C8 can only be <9>
R5C8 can only be <7>
R6C3 can only be <1>
R6C5 can only be <6>
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