Sep 19 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R7C9 is the only square in row 7 that can be <1>
R7C8 is the only square in row 7 that can be <8>
R8C7 is the only square in row 8 that can be <9>
R1C4 is the only square in row 1 that can be <9>
R1C6 is the only square in row 1 that can be <1>
R3C9 is the only square in row 3 that can be <9>
R5C4 is the only square in row 5 that can be <1>
R6C7 is the only square in row 6 that can be <1>
R6C9 is the only square in row 6 that can be <4>
R1C8 is the only square in block 3 that can be <3>
Intersection of row 1 with block 1. The value <7> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <7> from <34567> leaving <3456>
Intersection of row 6 with block 5. The value <7> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <7> from <567> leaving <56>
R4C5 - removing <7> from <23679> leaving <2369>
Squares R4C4 and R4C7 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C3 - removing <56> from <23569> leaving <239>
R4C5 - removing <6> from <2369> leaving <239>
R4C8 - removing <5> from <57> leaving <7>
R4C9 - removing <6> from <367> leaving <37>
R4C9 can only be <3>
R9C8 can only be <4>
R5C9 can only be <6>
R2C9 can only be <2>
R4C7 can only be <5>
R9C7 can only be <2>
R2C8 can only be <5>
R2C3 can only be <6>
R9C9 can only be <7>
R4C4 can only be <6>
R2C4 can only be <4>
R1C2 can only be <4>
R9C4 can only be <5>
R9C3 can only be <3>
R7C4 can only be <7>
R1C7 can only be <6>
R8C2 can only be <8>
R3C7 can only be <4>
R7C3 can only be <5>
R8C6 can only be <2>
R8C5 can only be <4>
R5C6 can only be <5>
R9C2 can only be <6>
R6C6 can only be <7>
R3C6 can only be <6>
R6C3 can only be <9>
R8C1 can only be <7>
R7C5 can only be <6>
R9C6 can only be <8>
R7C1 can only be <4>
R3C5 can only be <7>
R6C5 can only be <3>
R4C3 can only be <2>
R6C2 can only be <5>
R5C5 can only be <2>
R1C1 can only be <2>
R1C3 can only be <7>
R5C1 can only be <3>
R4C5 can only be <9>
R3C1 can only be <5>
R6C1 can only be <6>
R3C2 can only be <3>
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