Jul 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 is the only square in row 4 that can be <5>
R3C9 can only be <4>
R9C9 is the only square in row 9 that can be <7>
R8C8 is the only square in column 8 that can be <4>
R8C2 can only be <1>
R5C8 is the only square in column 8 that can be <2>
Intersection of row 7 with block 7. The value <6> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <6> from <2469> leaving <249>
R9C3 - removing <6> from <469> leaving <49>
Intersection of row 8 with block 8. The values <235> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R9C4 - removing <2> from <1268> leaving <168>
R9C6 - removing <2> from <268> leaving <68>
Intersection of column 8 with block 6. The value <1> 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 <1> from <168> leaving <68>
R5C9 - removing <1> from <138> leaving <38>
R6C9 - removing <1> from <1389> leaving <389>
Squares R2C6<468>, R4C6<38>, R6C6<348> and R9C6<68> in column 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <346> from <23456> leaving <25>
R8C6 - removing <3> from <235> leaving <25>
Intersection of column 6 with block 5. The value <3> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 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 <3> from <1378> leaving <178>
R5C5 - removing <3> from <13478> leaving <1478>
R6C4 - removing <3> from <138> leaving <18>
Squares R2C4<678>, R4C4<178>, R6C4<18> and R9C4<168> in column 4 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1678>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C4 - removing <6> from <236> leaving <23>
Intersection of block 2 with row 2. The values <67> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain these values.
R2C2 - removing <6> from <4689> leaving <489>
R2C8 - removing <6> from <69> leaving <9>
R4C8 can only be <1>
R1C9 can only be <1>
R6C8 can only be <6>
R5C7 can only be <8>
R7C9 can only be <8>
R5C9 can only be <3>
R6C9 can only be <9>
R5C2 is the only square in column 2 that can be <6>
R5C3 can only be <4>
R9C3 can only be <9>
R6C2 can only be <8>
R6C4 can only be <1>
R2C2 can only be <4>
R4C2 can only be <9>
R6C1 can only be <3>
R5C5 can only be <7>
R7C3 can only be <6>
R5C1 can only be <1>
R2C5 can only be <8>
R4C4 can only be <8>
R6C6 can only be <4>
R3C1 can only be <6>
R4C1 can only be <7>
R7C1 can only be <2>
R1C3 can only be <3>
R1C4 can only be <2>
R3C3 can only be <8>
R1C6 can only be <5>
R8C4 can only be <3>
R1C5 can only be <4>
R1C7 can only be <6>
R8C6 can only be <2>
R1C1 can only be <9>
R3C7 can only be <5>
R2C6 can only be <6>
R3C5 can only be <3>
R9C5 can only be <1>
R2C4 can only be <7>
R9C6 can only be <8>
R8C5 can only be <5>
R4C6 can only be <3>
R9C4 can only be <6>
R7C7 can only be <1>
R9C1 can only be <4>
R7C5 can only be <9>
R9C7 can only be <2>
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