Jan 01 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <1>
R4C7 is the only square in row 4 that can be <7>
R4C9 is the only square in row 4 that can be <2>
R6C3 is the only square in column 3 that can be <4>
R6C8 can only be <1>
R6C1 is the only square in row 6 that can be <5>
R5C4 is the only square in column 4 that can be <7>
R5C5 can only be <5>
R5C6 can only be <1>
R1C4 is the only square in block 2 that can be <5>
R7C4 can only be <6>
R3C4 can only be <3>
R5C2 is the only square in block 4 that can be <3>
R5C1 is the only square in block 4 that can be <6>
Intersection of row 2 with block 3. The value <4> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <4> from <2478> leaving <278>
Intersection of column 9 with block 9. The value <8> 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.
R8C8 - removing <8> from <248> leaving <24>
Squares R7C5<24>, R7C6<245> and R9C6<25> in block 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <245>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <24> from <2478> leaving <78>
R9C5 - removing <2> from <278> leaving <78>
Intersection of row 8 with block 9. The value <4> 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 <4> from <1245> leaving <125>
R7C8 - removing <4> from <249> leaving <29>
Squares R1C7<23>, R2C7<234> and R2C9<34> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <234>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <2> from <278> leaving <78>
R3C8 - removing <2> from <278> leaving <78>
Intersection of column 8 with block 9. The value <2> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 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 <2> from <125> leaving <15>
R8C7 - removing <2> from <1245> leaving <145>
R9C7 - removing <2> from <256> leaving <56>
Squares R8C1<27>, R8C5<78>, R8C8<24> and R8C9<48> in row 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <7> from <157> leaving <15>
R8C7 - removing <4> from <145> leaving <15>
R2C7 is the only square in column 7 that can be <4>
R2C9 can only be <3>
R6C9 can only be <6>
R1C7 can only be <2>
R6C7 can only be <3>
R1C5 can only be <6>
R1C3 is the only square in row 1 that can be <3>
R3C3 is the only square in row 3 that can be <6>
R3C8 is the only square in row 3 that can be <7>
R1C8 can only be <8>
R1C1 can only be <7>
R8C1 can only be <2>
R8C8 can only be <4>
R2C1 can only be <9>
R8C9 can only be <8>
R5C8 can only be <9>
R8C5 can only be <7>
R9C9 can only be <9>
R9C2 can only be <5>
R5C9 can only be <4>
R7C8 can only be <2>
R2C3 can only be <5>
R4C1 can only be <8>
R2C2 can only be <2>
R8C3 can only be <1>
R9C3 can only be <7>
R7C5 can only be <4>
R8C7 can only be <5>
R4C3 can only be <9>
R9C5 can only be <8>
R7C7 can only be <1>
R9C7 can only be <6>
R9C6 can only be <2>
R7C2 can only be <9>
R3C6 can only be <4>
R3C2 can only be <8>
R3C5 can only be <2>
R7C6 can only be <5>
R4C2 can only be <1>
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