Jul 23 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <4>
R8C6 is the only square in row 8 that can be <5>
R2C3 is the only square in row 2 that can be <5>
R2C1 is the only square in row 2 that can be <7>
R6C3 is the only square in row 6 that can be <7>
R9C1 is the only square in column 1 that can be <9>
R6C4 is the only square in column 4 that can be <4>
R1C9 is the only square in column 9 that can be <2>
R1C5 is the only square in row 1 that can be <5>
R3C8 is the only square in row 3 that can be <5>
R6C2 is the only square in row 6 that can be <5>
R4C9 is the only square in row 4 that can be <5>
R4C7 is the only square in row 4 that can be <7>
R7C8 is the only square in column 8 that can be <3>
R8C4 is the only square in row 8 that can be <3>
Intersection of row 2 with block 2. The value <2> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <2> from <23689> leaving <3689>
R3C6 - removing <2> from <123689> leaving <13689>
Intersection of row 4 with block 5. The value <3> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <3> from <23689> leaving <2689>
Intersection of row 8 with block 9. The value <9> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. 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 <9> from <1689> leaving <168>
R7C9 - removing <9> from <1679> leaving <167>
Intersection of column 8 with block 6. The value <9> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C7 - removing <9> from <14689> leaving <1468>
R5C9 - removing <9> from <169> leaving <16>
R8C9 is the only square in column 9 that can be <9>
Intersection of block 6 with row 5. The values <14> 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 these values.
R5C1 - removing <1> from <1236> leaving <236>
R5C2 - removing <1> from <1268> leaving <268>
R5C3 - removing <1> from <1236> leaving <236>
Intersection of block 3 with column 7. The values <369> only appears in one or more of squares R1C7, R2C7 and R3C7 of block 3. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain these values.
R5C7 - removing <6> from <1468> leaving <148>
R7C7 - removing <6> from <168> leaving <18>
R8C7 - removing <6> from <46> leaving <4>
R8C3 can only be <6>
R5C8 is the only square in row 5 that can be <4>
R5C5 is the only square in row 5 that can be <9>
R6C8 is the only square in row 6 that can be <9>
R7C4 is the only square in row 7 that can be <9>
R9C3 is the only square in row 9 that can be <4>
R9C9 is the only square in row 9 that can be <1>
R5C9 can only be <6>
R7C7 can only be <8>
R7C9 can only be <7>
R4C8 can only be <8>
R5C7 can only be <1>
R9C8 can only be <6>
R5C2 is the only square in row 5 that can be <8>
R7C5 is the only square in row 7 that can be <6>
R6C5 can only be <8>
R3C5 can only be <3>
R4C5 can only be <2>
R9C5 can only be <7>
R2C7 is the only square in row 2 that can be <3>
R1C1 is the only square in row 1 that can be <3>
R5C1 can only be <2>
R5C3 can only be <3>
R3C6 is the only square in row 3 that can be <8>
R9C6 can only be <2>
R9C4 can only be <8>
R2C6 can only be <6>
R2C4 can only be <2>
R6C6 can only be <1>
R1C4 can only be <1>
R6C1 can only be <6>
R1C6 can only be <9>
R4C6 can only be <3>
R4C4 can only be <6>
R1C7 can only be <6>
R3C7 can only be <9>
R4C2 can only be <1>
R3C1 can only be <1>
R3C3 can only be <2>
R3C2 can only be <6>
R7C3 can only be <1>
R7C2 can only be <2>
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