Dec 04 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C3 can only be <6>
R6C3 can only be <3>
R6C7 can only be <5>
R4C7 can only be <2>
R5C3 can only be <1>
R4C5 can only be <4>
R5C1 can only be <4>
R6C5 can only be <8>
R7C1 can only be <7>
R9C3 can only be <8>
R9C1 can only be <1>
R1C3 can only be <7>
R1C1 can only be <8>
R3C1 can only be <9>
R2C4 is the only square in row 2 that can be <8>
R3C5 is the only square in row 3 that can be <3>
R9C9 is the only square in row 9 that can be <3>
Intersection of row 1 with block 2. The value <1> 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 this value.
R2C5 - removing <1> from <159> leaving <59>
R2C6 - removing <1> from <1459> leaving <459>
Intersection of row 3 with block 3. The value <2> 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.
R1C9 - removing <2> from <256> leaving <56>
Intersection of column 8 with block 9. The value <6> 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.
R7C9 - removing <6> from <269> leaving <29>
R9C7 - removing <6> from <469> leaving <49>
R9C5 is the only square in row 9 that can be <6>
R9C4 is the only square in row 9 that can be <7>
R5C5 is the only square in row 5 that can be <7>
Squares R7C5 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C8 - removing <2> from <246> leaving <46>
Squares R7C2, R7C8, R8C2 and R8C8 form a Type-1 Unique Rectangle on <46>.
R8C8 - removing <46> from <246> leaving <2>
R3C8 can only be <1>
R7C9 can only be <9>
R3C2 can only be <5>
R2C8 can only be <4>
R7C5 can only be <2>
R5C9 can only be <6>
R9C7 can only be <4>
R9C6 can only be <9>
R1C7 can only be <6>
R7C8 can only be <6>
R1C9 can only be <5>
R5C7 can only be <9>
R3C9 can only be <2>
R2C2 can only be <1>
R1C5 can only be <1>
R7C2 can only be <4>
R2C6 can only be <5>
R8C5 can only be <5>
R2C5 can only be <9>
R5C6 can only be <2>
R5C4 can only be <5>
R1C6 can only be <4>
R8C2 can only be <6>
R8C4 can only be <4>
R1C4 can only be <2>
R8C6 can only be <1>
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