Feb 12 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <7>
R4C8 can only be <5>
R1C2 is the only square in row 1 that can be <7>
R3C5 is the only square in row 3 that can be <7>
R5C5 is the only square in row 5 that can be <9>
R7C8 is the only square in row 7 that can be <7>
R1C9 is the only square in column 9 that can be <5>
R5C2 is the only square in block 4 that can be <2>
Squares R5C7 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <34> from <1347> leaving <17>
R5C6 - removing <4> from <145> leaving <15>
Intersection of row 1 with block 3. The value <3> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <3> from <12346> leaving <1246>
R2C8 - removing <3> from <12348> leaving <1248>
R3C7 - removing <3> from <1346> leaving <146>
R3C8 - removing <3> from <13489> leaving <1489>
R3C9 - removing <3> from <3469> leaving <469>
R3C2 is the only square in row 3 that can be <3>
Intersection of row 3 with block 3. The value <6> 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.
R2C7 - removing <6> from <1246> leaving <124>
Intersection of row 4 with block 5. The values <268> 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 these values.
R6C5 - removing <8> from <358> leaving <35>
R6C6 - removing <8> from <458> leaving <45>
Intersection of row 9 with block 7. The value <5> 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.
R8C2 - removing <5> from <1568> leaving <168>
R8C3 - removing <5> from <34568> leaving <3468>
Intersection of column 2 with block 7. The values <19> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <9> from <2489> leaving <248>
R9C1 - removing <9> from <259> leaving <25>
Intersection of column 9 with block 9. The value <3> 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.
R8C7 - removing <3> from <12346> leaving <1246>
R8C8 - removing <3> from <1234> leaving <124>
R9C8 - removing <3> from <1239> leaving <129>
Squares R3C6<14>, R5C6<15> and R6C6<45> in column 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <4> from <24> leaving <2>
R8C6 - removing <15> from <12568> leaving <268>
R8C5 is the only square in row 8 that can be <5>
R6C5 can only be <3>
R2C5 can only be <1>
R3C6 can only be <4>
R6C6 can only be <5>
R2C4 can only be <3>
R6C2 can only be <8>
R5C6 can only be <1>
R5C4 can only be <7>
R6C3 can only be <7>
R6C4 can only be <4>
R5C3 can only be <5>
Squares R1C7 and R5C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <4> from <24> leaving <2>
R8C7 - removing <4> from <1246> leaving <126>
R8C8 is the only square in row 8 that can be <2>
Squares R8C2 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <6> from <3468> leaving <348>
R8C6 - removing <6> from <68> leaving <8>
R8C9 - removing <6> from <346> leaving <34>
R4C6 can only be <6>
R7C5 can only be <2>
R4C4 can only be <2>
R4C5 can only be <8>
R9C1 is the only square in row 9 that can be <2>
R9C2 is the only square in row 9 that can be <5>
R2C2 can only be <6>
R8C2 can only be <1>
R8C7 can only be <6>
R7C2 can only be <9>
R3C7 can only be <1>
R7C9 can only be <4>
R7C1 can only be <8>
R8C9 can only be <3>
R8C3 can only be <4>
R9C9 can only be <9>
R9C8 can only be <1>
R3C9 can only be <6>
R7C3 can only be <6>
R3C1 can only be <9>
R7C4 can only be <1>
R9C3 can only be <3>
R9C4 can only be <6>
R2C3 can only be <8>
R2C8 can only be <4>
R2C1 can only be <5>
R5C8 can only be <3>
R1C7 can only be <3>
R3C8 can only be <8>
R1C1 can only be <4>
R5C7 can only be <4>
R1C8 can only be <9>
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