Jul 21 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 is the only square in row 4 that can be <4>
R1C3 is the only square in row 1 that can be <4>
R3C2 can only be <3>
R3C9 can only be <9>
R3C8 is the only square in row 3 that can be <4>
R4C6 is the only square in row 4 that can be <7>
R5C2 is the only square in row 5 that can be <6>
R8C2 can only be <4>
R5C8 is the only square in row 5 that can be <8>
R5C5 is the only square in row 5 that can be <2>
R6C1 is the only square in column 1 that can be <8>
R6C9 is the only square in column 9 that can be <6>
R6C4 is the only square in block 5 that can be <9>
Squares R4C2 and R4C9 in row 4 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.
R4C3 - removing <12> from <1259> leaving <59>
Squares R2C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C3 - removing <7> from <12579> leaving <1259>
R8C3 - removing <7> from <679> leaving <69>
R9C3 - removing <7> from <12567> leaving <1256>
Squares R4C1 and R4C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C3 - removing <5> from <125> leaving <12>
Intersection of row 2 with block 3. The values <23> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C7 - removing <3> from <1378> leaving <178>
R1C9 - removing <3> from <13> leaving <1>
R4C9 can only be <2>
R4C2 can only be <1>
R2C9 can only be <3>
R6C8 can only be <5>
R6C7 can only be <1>
R7C2 can only be <2>
R6C3 can only be <2>
R7C8 can only be <7>
R7C7 can only be <3>
R2C8 can only be <2>
R8C7 can only be <6>
R8C3 can only be <9>
R9C7 can only be <2>
R8C5 can only be <7>
R4C3 can only be <5>
R7C1 can only be <5>
R8C1 can only be <3>
R9C5 can only be <5>
R2C5 can only be <8>
R2C3 can only be <7>
R1C5 can only be <9>
R4C1 can only be <9>
R7C3 can only be <1>
R7C6 can only be <9>
R9C3 can only be <6>
R1C6 can only be <3>
R9C1 can only be <7>
R1C4 can only be <7>
R9C6 can only be <1>
R2C7 can only be <5>
R3C3 can only be <8>
R3C7 can only be <7>
R3C4 can only be <5>
R1C7 can only be <8>
R9C4 can only be <3>
R5C6 can only be <5>
R5C4 can only be <1>
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