Aug 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <7>
R2C7 is the only square in row 2 that can be <5>
R2C5 is the only square in row 2 that can be <7>
R2C3 is the only square in row 2 that can be <9>
R7C3 can only be <4>
R3C2 is the only square in row 3 that can be <4>
R4C2 is the only square in row 4 that can be <7>
R6C8 is the only square in row 6 that can be <4>
R4C1 is the only square in row 4 that can be <4>
R8C7 is the only square in row 8 that can be <4>
R9C4 is the only square in row 9 that can be <4>
R9C3 is the only square in row 9 that can be <7>
R8C3 can only be <2>
R8C6 can only be <1>
R9C2 can only be <9>
R8C5 can only be <3>
R9C7 can only be <6>
R9C8 can only be <5>
R9C6 can only be <2>
R7C8 can only be <9>
R7C7 can only be <3>
R8C9 can only be <7>
R7C4 can only be <6>
R7C5 can only be <5>
R4C4 is the only square in row 4 that can be <3>
R5C9 is the only square in row 5 that can be <5>
R6C9 can only be <3>
R6C6 is the only square in row 6 that can be <5>
Squares R5C1 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <2> from <236> leaving <36>
R5C3 - removing <1> from <1368> leaving <368>
R5C5 - removing <12> from <1269> leaving <69>
R5C7 - removing <12> from <1289> leaving <89>
Squares R1C7 and R3C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C7 - removing <12> from <1289> leaving <89>
Squares R4C6 and R4C7 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <9> from <129> leaving <12>
Intersection of column 6 with block 2. The value <6> only appears in one or more of squares R1C6, R2C6 and R3C6 of column 6. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <6> from <1269> leaving <129>
Squares R2C4 and R4C5 form a remote naked pair. <12> can be removed from any square that is common to their groups.
R3C5 - removing <12> from <129> leaving <9>
R6C4 - removing <12> from <128> leaving <8>
R3C6 can only be <6>
R5C5 can only be <6>
R3C3 can only be <1>
R1C6 can only be <8>
R5C2 can only be <3>
R4C6 can only be <9>
R3C7 can only be <2>
R6C3 can only be <6>
R2C1 can only be <2>
R1C7 can only be <1>
R4C7 can only be <8>
R5C7 can only be <9>
R5C3 can only be <8>
R6C2 can only be <2>
R1C3 can only be <3>
R1C4 can only be <2>
R2C4 can only be <1>
R5C1 can only be <1>
R1C2 can only be <6>
R5C8 can only be <2>
R4C8 can only be <1>
R6C5 can only be <1>
R4C5 can only be <2>
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