Jul 08 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 is the only square in row 4 that can be <4>
R2C4 is the only square in row 2 that can be <4>
R4C3 is the only square in row 4 that can be <6>
R4C7 is the only square in row 4 that can be <9>
R1C9 is the only square in row 1 that can be <9>
R5C9 is the only square in row 5 that can be <4>
R5C4 is the only square in row 5 that can be <6>
R8C2 is the only square in row 8 that can be <4>
R8C4 is the only square in row 8 that can be <9>
R7C2 is the only square in row 7 that can be <9>
R9C5 is the only square in row 9 that can be <7>
R1C1 is the only square in row 1 that can be <7>
R2C6 is the only square in row 2 that can be <7>
R3C1 is the only square in column 1 that can be <6>
R8C3 is the only square in block 7 that can be <5>
R7C6 is the only square in block 8 that can be <3>
Intersection of row 9 with block 7. The value <2> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <2> from <128> leaving <18>
R9C1 is the only square in column 1 that can be <2>
Intersection of column 3 with block 1. The value <3> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <3> from <135> leaving <15>
R3C2 - removing <3> from <1235> leaving <125>
Intersection of row 3 with block 3. The value <3> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <3> from <35> leaving <5>
R2C7 - removing <3> from <13568> leaving <1568>
R2C8 - removing <3> from <13568> leaving <1568>
R6C7 can only be <1>
R4C8 can only be <3>
R4C2 can only be <1>
R2C2 can only be <5>
R5C1 can only be <8>
R7C1 can only be <1>
R6C3 can only be <2>
R6C2 can only be <7>
R1C3 can only be <3>
R7C9 can only be <5>
R9C3 can only be <8>
R9C7 can only be <3>
R9C9 can only be <1>
R3C9 can only be <3>
R1C5 can only be <2>
R2C3 can only be <1>
R3C4 can only be <8>
R3C2 can only be <2>
R3C6 can only be <5>
R3C8 can only be <1>
R7C4 can only be <2>
R2C5 can only be <3>
R5C6 can only be <1>
R5C5 can only be <5>
R8C6 can only be <8>
R6C8 can only be <5>
R5C2 can only be <3>
R6C5 can only be <8>
R5C8 can only be <7>
R7C8 can only be <8>
R2C8 can only be <6>
R8C7 can only be <6>
R8C5 can only be <1>
R8C8 can only be <2>
R2C7 can only be <8>
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