Jun 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C6 can only be <7>
R7C6 can only be <6>
R9C6 can only be <8>
R6C6 can only be <2>
R2C8 is the only square in row 2 that can be <9>
R3C4 is the only square in row 3 that can be <8>
R5C2 is the only square in row 5 that can be <2>
R6C7 is the only square in row 6 that can be <9>
R7C3 is the only square in row 7 that can be <9>
R4C1 is the only square in row 4 that can be <9>
R7C2 is the only square in row 7 that can be <7>
R8C5 is the only square in row 8 that can be <9>
R9C8 is the only square in row 9 that can be <2>
R1C9 is the only square in row 1 that can be <2>
R8C2 is the only square in column 2 that can be <4>
R8C7 is the only square in row 8 that can be <3>
R5C8 is the only square in row 5 that can be <3>
R5C5 is the only square in row 5 that can be <8>
R4C3 is the only square in block 4 that can be <1>
Squares R3C1 and R3C3 in row 3 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 row.
R3C7 - removing <6> from <146> leaving <14>
R3C8 - removing <7> from <147> leaving <14>
R1C8 is the only square in column 8 that can be <7>
Squares R3C7 and R7C7 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.
R1C7 - removing <1> from <156> leaving <56>
R5C7 - removing <4> from <456> leaving <56>
R5C9 is the only square in row 5 that can be <4>
R7C9 can only be <1>
R4C8 can only be <8>
R7C7 can only be <4>
R6C8 can only be <1>
R3C8 can only be <4>
R3C7 can only be <1>
R6C2 is the only square in row 6 that can be <8>
Squares R3C1 and R3C3 in block 1 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.
R1C2 - removing <6> from <356> leaving <35>
R2C3 - removing <67> from <3567> leaving <35>
Squares R3C1, R3C3, R5C1 and R5C3 form a Type-2 Unique Rectangle on <67>.
R4C2 - removing <5> from <56> leaving <6>
R5C7 - removing <5> from <56> leaving <6>
R1C7 can only be <5>
R6C9 can only be <5>
R2C9 can only be <6>
R1C2 can only be <3>
R9C2 can only be <5>
R2C3 can only be <5>
R5C3 can only be <7>
R5C1 can only be <5>
R3C3 can only be <6>
R9C5 can only be <1>
R8C1 can only be <1>
R9C1 can only be <6>
R1C5 can only be <6>
R8C4 can only be <5>
R1C4 can only be <1>
R6C5 can only be <7>
R3C1 can only be <7>
R9C3 can only be <3>
R6C4 can only be <6>
R2C5 can only be <4>
R4C4 can only be <3>
R2C6 can only be <3>
R4C5 can only be <5>
R2C4 can only be <7>
R4C6 can only be <4>
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