Jan 22 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <3>
R5C8 can only be <2>
R5C2 can only be <5>
R6C9 can only be <1>
R6C6 can only be <8>
R6C8 can only be <7>
R4C9 can only be <5>
R6C4 can only be <9>
R4C8 can only be <3>
R6C1 can only be <4>
R6C2 can only be <2>
R3C2 is the only square in row 3 that can be <3>
R7C7 is the only square in row 7 that can be <3>
Intersection of row 3 with block 1. The value <5> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C3 - removing <5> from <4579> leaving <479>
Intersection of row 3 with block 3. The value <1> 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 <1> from <179> leaving <79>
R2C8 - removing <1> from <1489> leaving <489>
Intersection of row 7 with block 7. The values <56> 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 these values.
R8C2 - removing <6> from <469> leaving <49>
R8C3 - removing <5> from <12459> leaving <1249>
R9C1 - removing <5> from <57> leaving <7>
R9C3 - removing <5> from <12457> leaving <1247>
R4C1 can only be <9>
R4C2 can only be <7>
Intersection of row 7 with block 9. The value <8> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C8 - removing <8> from <1489> leaving <149>
Squares R1C4<368>, R1C6<36> and R2C5<68> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <68> from <1568> leaving <15>
R2C6 - removing <6> from <156> leaving <15>
Squares R1C1<68>, R1C4<368> and R1C6<36> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C9 - removing <68> from <2468> leaving <24>
R3C9 is the only square in column 9 that can be <6>
R7C9 is the only square in column 9 that can be <8>
R7C8 can only be <9>
R7C2 can only be <6>
R7C1 can only be <5>
R7C3 can only be <2>
R3C1 can only be <8>
R3C8 can only be <1>
R1C1 can only be <6>
R3C7 can only be <7>
R8C8 can only be <4>
R8C2 can only be <9>
R2C8 can only be <8>
R9C9 can only be <2>
R1C9 can only be <4>
R1C6 can only be <3>
R1C4 can only be <8>
R9C6 can only be <5>
R1C3 can only be <9>
R2C5 can only be <6>
R3C3 can only be <5>
R2C7 can only be <9>
R8C3 can only be <1>
R2C2 can only be <4>
R8C7 can only be <5>
R9C3 can only be <4>
R9C7 can only be <1>
R9C4 can only be <3>
R2C6 can only be <1>
R1C7 can only be <2>
R2C3 can only be <7>
R8C4 can only be <6>
R8C5 can only be <8>
R2C4 can only be <5>
R4C6 can only be <6>
R4C4 can only be <1>
R8C6 can only be <2>
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