Sep 21 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C3 can only be <3>
R4C3 can only be <6>
R8C3 can only be <5>
R5C3 can only be <9>
R1C9 is the only square in row 1 that can be <6>
R1C1 is the only square in row 1 that can be <5>
R3C8 is the only square in row 3 that can be <4>
R3C6 is the only square in row 3 that can be <6>
R5C4 is the only square in row 5 that can be <8>
R8C5 is the only square in column 5 that can be <4>
R8C1 can only be <3>
R8C2 can only be <2>
R5C7 is the only square in column 7 that can be <6>
R5C8 is the only square in row 5 that can be <5>
R7C9 is the only square in row 7 that can be <5>
R2C7 is the only square in row 2 that can be <5>
R8C9 is the only square in block 9 that can be <1>
R8C6 can only be <7>
Squares R4C7 and R6C7 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C8 - removing <7> from <237> leaving <23>
R4C9 - removing <7> from <2378> leaving <238>
R6C9 - removing <7> from <278> leaving <28>
Intersection of row 5 with block 5. The value <3> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <3> from <123> leaving <12>
Intersection of column 4 with block 2. The value <3> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <3> from <37> leaving <7>
R2C5 - removing <3> from <1237> leaving <127>
R5C2 is the only square in row 5 that can be <7>
R4C7 is the only square in row 4 that can be <7>
R6C7 can only be <1>
R6C2 can only be <4>
R6C1 can only be <8>
R7C2 can only be <9>
R1C2 can only be <3>
R9C1 can only be <6>
R7C1 can only be <4>
R1C4 can only be <9>
R3C2 can only be <1>
R3C4 can only be <3>
R6C9 can only be <2>
R4C1 can only be <1>
R6C4 can only be <7>
R9C9 can only be <7>
R4C8 can only be <3>
R9C8 can only be <2>
R3C9 can only be <9>
R3C1 can only be <7>
R2C9 can only be <3>
R4C6 can only be <2>
R7C6 can only be <1>
R4C9 can only be <8>
R2C8 can only be <7>
R7C4 can only be <2>
R5C6 can only be <3>
R9C5 can only be <3>
R7C8 can only be <6>
R2C1 can only be <9>
R5C5 can only be <1>
R9C6 can only be <9>
R2C4 can only be <1>
R2C5 can only be <2>
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