Jan 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <5>
Intersection of block 4 with row 5. The value <5> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C6 - removing <5> from <158> leaving <18>
R5C9 - removing <5> from <1569> leaving <169>
Intersection of column 9 with block 9. The value <5> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <5> from <4578> leaving <478>
Intersection of block 6 with row 5. The value <9> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C1 - removing <9> from <3569> leaving <356>
R5C2 - removing <9> from <359> leaving <35>
R5C5 - removing <9> from <1349> leaving <134>
R9C2 is the only square in column 2 that can be <9>
R7C9 is the only square in row 7 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R7C1 is the only square in row 7 that can be <5>
R5C2 is the only square in row 5 that can be <5>
R7C3 is the only square in row 7 that can be <3>
R8C9 is the only square in row 8 that can be <5>
R3C1 is the only square in column 1 that can be <9>
R3C7 is the only square in row 3 that can be <4>
R1C1 is the only square in row 1 that can be <4>
R3C9 is the only square in row 3 that can be <7>
R1C2 is the only square in row 1 that can be <7>
R8C2 can only be <2>
R8C5 can only be <7>
R2C2 can only be <3>
R7C6 can only be <8>
R2C1 can only be <8>
R7C4 can only be <4>
R7C7 can only be <7>
R5C6 can only be <1>
R8C1 can only be <6>
R5C9 can only be <6>
R3C6 can only be <2>
R4C6 can only be <5>
R5C1 can only be <3>
R9C9 can only be <1>
R6C7 can only be <5>
R4C7 can only be <1>
R9C5 can only be <2>
R8C8 can only be <8>
R9C1 can only be <7>
R9C3 can only be <8>
R1C8 can only be <1>
R2C5 can only be <1>
R6C5 can only be <9>
R9C7 can only be <6>
R2C9 can only be <2>
R1C3 can only be <2>
R1C7 can only be <8>
R2C8 can only be <6>
R9C8 can only be <4>
R1C9 can only be <3>
R3C3 can only be <1>
R3C4 can only be <3>
R6C6 can only be <7>
R5C4 can only be <8>
R5C5 can only be <4>
R6C3 can only be <6>
R4C5 can only be <3>
R4C4 can only be <6>
R4C3 can only be <9>
R6C4 can only be <2>
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