Jul 04 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C7 is the only square in row 3 that can be <3>
R7C9 is the only square in row 7 that can be <8>
R7C3 is the only square in row 7 that can be <6>
R9C7 is the only square in row 9 that can be <6>
R9C5 is the only square in row 9 that can be <1>
R8C1 is the only square in column 1 that can be <9>
R7C2 is the only square in block 7 that can be <2>
R7C4 can only be <5>
Squares R1C7 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <27> from <2478> leaving <48>
R1C5 - removing <27> from <2478> leaving <48>
Squares R1C7 and R1C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C9 - removing <7> from <567> leaving <56>
R3C8 - removing <27> from <2567> leaving <56>
Squares R7C5 and R7C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C6 - removing <7> from <247> leaving <24>
Intersection of row 4 with block 5. The value <4> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <4> from <1248> leaving <128>
R5C6 - removing <4> from <12349> leaving <1239>
Squares R9C2, R9C3, R6C2 and R6C3 form a Type-3 Unique Rectangle on <57>. Upon close inspection, it is clear that:
(R6C2 or R6C3)<12> and R6C4<12> form a naked pair on <12> in row 6. No other squares in the row can contain these possibilities
R6C1 - removing <2> from <2357> leaving <357>
R6C5 - removing <2> from <29> leaving <9>
(R6C2 or R6C3)<12>, R6C5<29> and R6C4<12> form a naked triplet on <129> in row 6. No other squares in the row can contain these possibilities
R6C9 - removing <9> from <3579> leaving <357>
R7C5 can only be <7>
R7C6 can only be <9>
R5C9 is the only square in row 5 that can be <9>
R5C8 is the only square in row 5 that can be <6>
R3C8 can only be <5>
R2C9 can only be <6>
R3C4 is the only square in row 3 that can be <6>
R5C4 is the only square in column 4 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R3C5 is the only square in row 3 that can be <8>
R1C5 can only be <4>
R1C3 can only be <8>
R4C5 can only be <2>
R4C8 can only be <1>
R6C4 can only be <1>
R4C7 can only be <5>
R8C8 can only be <7>
R2C4 can only be <2>
R5C6 can only be <3>
R8C9 can only be <5>
R1C8 can only be <2>
R8C7 can only be <1>
R4C9 can only be <3>
R1C7 can only be <7>
R8C4 can only be <4>
R3C6 can only be <7>
R3C1 can only be <2>
R2C6 can only be <1>
R4C6 can only be <4>
R6C9 can only be <7>
R6C2 can only be <5>
R5C7 can only be <2>
R8C6 can only be <2>
R5C1 can only be <7>
R2C1 can only be <5>
R5C3 can only be <4>
R6C1 can only be <3>
R6C3 can only be <2>
R9C2 can only be <7>
R9C3 can only be <5>
R2C2 can only be <4>
R2C3 can only be <7>
R5C2 can only be <1>
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