Sep 05 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <3>
R3C5 can only be <9>
R5C4 is the only square in row 5 that can be <8>
R5C5 is the only square in row 5 that can be <1>
R5C7 is the only square in row 5 that can be <7>
R3C7 can only be <3>
R7C7 can only be <6>
R7C5 can only be <2>
R9C6 can only be <6>
R8C5 can only be <7>
R6C5 can only be <5>
R9C4 can only be <1>
R4C5 can only be <6>
R6C4 is the only square in row 6 that can be <7>
R6C6 is the only square in row 6 that can be <9>
R8C1 is the only square in row 8 that can be <6>
R1C3 is the only square in row 1 that can be <6>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <4> from <13457> leaving <1357>
R1C2 - removing <4> from <1345> leaving <135>
R1C8 - removing <4> from <145> leaving <15>
R1C9 - removing <4> from <14579> leaving <1579>
Squares R1C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <15> from <1458> leaving <48>
R5C8 - removing <5> from <245> leaving <24>
R9C8 - removing <5> from <258> leaving <28>
R4C9 is the only square in block 6 that can be <5>
Intersection of row 2 with block 1. The value <5> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <5> from <1357> leaving <137>
R1C2 - removing <5> from <135> leaving <13>
Squares R8C8<15>, R8C9<19> and R9C7<59> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <159>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <1> from <13> leaving <3>
R9C9 - removing <9> from <2389> leaving <238>
R7C3 can only be <4>
R7C1 can only be <1>
R3C3 can only be <7>
R1C1 can only be <3>
R1C2 can only be <1>
R1C8 can only be <5>
R1C7 can only be <9>
R8C8 can only be <1>
R8C9 can only be <9>
R8C2 can only be <5>
R1C9 can only be <7>
R9C7 can only be <5>
R9C1 can only be <7>
R9C3 can only be <3>
R2C2 can only be <4>
R9C2 can only be <9>
R5C3 can only be <5>
R2C8 can only be <8>
R5C2 can only be <3>
R3C1 can only be <8>
R2C1 can only be <5>
R2C9 can only be <1>
R9C8 can only be <2>
R3C9 can only be <4>
R6C9 can only be <2>
R6C1 can only be <4>
R9C9 can only be <8>
R5C8 can only be <4>
R5C6 can only be <2>
R4C1 can only be <2>
R4C4 can only be <4>
R4C6 can only be <3>
R1C4 can only be <2>
R1C6 can only be <4>
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