Mar 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <2>
R8C3 can only be <9>
R8C7 can only be <3>
R7C8 can only be <8>
R7C5 is the only square in row 7 that can be <7>
R4C9 is the only square in row 4 that can be <7>
R5C7 can only be <9>
R2C7 can only be <7>
R2C9 is the only square in row 2 that can be <9>
R3C1 is the only square in row 3 that can be <7>
R7C9 is the only square in row 7 that can be <2>
R9C1 is the only square in row 9 that can be <3>
R3C9 is the only square in column 9 that can be <8>
R8C1 is the only square in block 7 that can be <8>
R8C4 can only be <4>
Squares R8C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C9 - removing <1> from <1346> leaving <346>
R6C9 - removing <1> from <146> leaving <46>
Intersection of column 2 with block 4. The values <18> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C1 - removing <1> from <12456> leaving <2456>
R6C1 - removing <1> from <12469> leaving <2469>
Squares R2C6<18>, R8C6<15> and R9C6<158> in column 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <1> from <147> leaving <47>
R5C6 - removing <8> from <478> leaving <47>
Squares R6C2<146>, R6C8<16> and R6C9<46> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <146>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <46> from <2469> leaving <29>
R6C5 - removing <4> from <249> leaving <29>
Squares R7C1, R7C2, R5C1 and R5C2 form a Type-4 Unique Rectangle on <56>.
R5C1 - removing <6> from <2456> leaving <245>
R5C2 - removing <6> from <14568> leaving <1458>
Squares R8C6, R8C9, R9C6 and R9C9 form a Type-1 Unique Rectangle on <15>.
R9C6 - removing <15> from <158> leaving <8>
R9C4 can only be <2>
R2C6 can only be <1>
R8C6 can only be <5>
R8C9 can only be <1>
R9C9 can only be <5>
R9C5 can only be <1>
R1C1 is the only square in row 1 that can be <1>
R2C4 is the only square in row 2 that can be <8>
R5C4 can only be <7>
R5C6 can only be <4>
R1C4 can only be <6>
R1C6 can only be <7>
R1C9 can only be <3>
R1C5 can only be <4>
R5C9 can only be <6>
R3C8 can only be <6>
R3C2 can only be <4>
R6C8 can only be <1>
R5C3 can only be <2>
R6C9 can only be <4>
R5C8 can only be <3>
R6C2 can only be <6>
R3C5 can only be <3>
R4C2 can only be <8>
R4C5 can only be <9>
R4C1 can only be <4>
R6C5 can only be <2>
R5C1 can only be <5>
R5C5 can only be <8>
R2C3 can only be <6>
R6C1 can only be <9>
R7C2 can only be <5>
R7C1 can only be <6>
R5C2 can only be <1>
R2C1 can only be <2>
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