Jun 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C9 can only be <9>
R9C3 can only be <1>
R9C9 can only be <6>
R2C2 is the only square in row 2 that can be <5>
R6C3 is the only square in row 6 that can be <5>
R8C8 is the only square in row 8 that can be <1>
R8C6 is the only square in row 8 that can be <5>
R3C2 is the only square in column 2 that can be <7>
R3C4 can only be <8>
R3C3 can only be <4>
R3C5 can only be <1>
R1C5 is the only square in row 1 that can be <4>
R8C5 is the only square in row 8 that can be <8>
Squares R5C4 and R5C5 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <69> from <13469> leaving <134>
R5C6 - removing <69> from <169> leaving <1>
R5C8 - removing <69> from <3469> leaving <34>
Squares R5C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <3> from <1369> leaving <169>
R6C2 - removing <4> from <1469> leaving <169>
Squares R5C4 and R5C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C6 - removing <69> from <2679> leaving <27>
R6C4 - removing <69> from <2679> leaving <27>
Squares R4C6 and R4C9 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C7 - removing <2> from <1239> leaving <139>
R4C8 - removing <2> from <2369> leaving <369>
Intersection of row 2 with block 2. The values <79> 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.
R1C6 - removing <9> from <269> leaving <26>
Squares R5C8 and R7C1 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R7C8 - removing <34> from <2349> leaving <29>
R7C1 is the only square in row 7 that can be <4>
R8C2 can only be <3>
R8C4 can only be <2>
R5C2 can only be <4>
R8C9 can only be <4>
R6C4 can only be <7>
R5C8 can only be <3>
R6C9 can only be <2>
R4C6 can only be <2>
R4C9 can only be <7>
R1C6 can only be <6>
R7C6 can only be <9>
R2C4 can only be <9>
R2C6 can only be <7>
R5C4 can only be <6>
R9C4 can only be <3>
R2C5 can only be <2>
R5C5 can only be <9>
R7C5 can only be <6>
R9C5 can only be <7>
R7C8 can only be <2>
R7C7 can only be <3>
R2C8 can only be <8>
R2C1 can only be <6>
R9C8 can only be <9>
R1C7 can only be <2>
R9C7 can only be <8>
R4C8 can only be <6>
R6C1 can only be <1>
R6C8 can only be <4>
R6C7 can only be <9>
R1C1 can only be <8>
R4C2 can only be <9>
R6C2 can only be <6>
R4C7 can only be <1>
R1C3 can only be <9>
R4C1 can only be <3>
R1C2 can only be <1>
R4C3 can only be <8>
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