Jan 08 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 is the only square in row 6 that can be <7>
R7C2 is the only square in row 7 that can be <2>
R5C3 is the only square in column 3 that can be <9>
R1C8 is the only square in column 8 that can be <6>
R1C2 is the only square in row 1 that can be <8>
R8C1 is the only square in column 1 that can be <8>
R9C8 is the only square in column 8 that can be <7>
Squares R1C4 and R6C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C4 - removing <1> from <18> leaving <8>
R8C4 - removing <3> from <2347> leaving <247>
R9C4 can only be <4>
R9C5 is the only square in row 9 that can be <8>
R2C6 is the only square in column 6 that can be <4>
R8C6 is the only square in column 6 that can be <2>
R8C4 can only be <7>
R2C4 can only be <2>
Intersection of row 1 with block 2. The values <135> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R2C5 - removing <5> from <579> leaving <79>
R3C5 - removing <5> from <579> leaving <79>
Intersection of column 1 with block 4. The values <24> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C2 - removing <4> from <1456> leaving <156>
R5C2 - removing <4> from <146> leaving <16>
R3C2 is the only square in column 2 that can be <4>
Intersection of column 7 with block 3. The value <5> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <5> from <589> leaving <89>
Intersection of block 8 with column 5. The value <3> only appears in one or more of squares R7C5, R8C5 and R9C5 of block 8. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R1C5 - removing <3> from <135> leaving <15>
R5C5 - removing <3> from <136> leaving <16>
Squares R5C2 and R5C5 in row 5 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.
R5C1 - removing <6> from <246> leaving <24>
R5C7 - removing <1> from <1238> leaving <238>
R5C9 - removing <1> from <148> leaving <48>
R8C7 is the only square in column 7 that can be <1>
R8C9 can only be <4>
R8C3 can only be <6>
R5C9 can only be <8>
R2C9 can only be <9>
R8C5 can only be <3>
R9C2 can only be <5>
R7C5 can only be <5>
R9C6 can only be <6>
R7C3 can only be <4>
R4C6 can only be <9>
R2C5 can only be <7>
R3C8 can only be <2>
R3C7 can only be <5>
R4C8 can only be <4>
R6C6 can only be <3>
R5C8 can only be <3>
R5C7 can only be <2>
R6C8 can only be <9>
R7C8 can only be <8>
R6C4 can only be <1>
R1C6 can only be <5>
R1C5 can only be <1>
R7C7 can only be <3>
R1C4 can only be <3>
R5C5 can only be <6>
R2C3 can only be <5>
R3C5 can only be <9>
R3C3 can only be <7>
R2C7 can only be <8>
R5C2 can only be <1>
R5C1 can only be <4>
R6C9 can only be <5>
R6C1 can only be <2>
R4C9 can only be <1>
R2C1 can only be <6>
R4C2 can only be <6>
R4C1 can only be <5>
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