Sep 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <8>
R3C6 is the only square in row 3 that can be <6>
R4C4 is the only square in row 4 that can be <8>
R3C3 is the only square in row 3 that can be <8>
R2C6 is the only square in row 2 that can be <8>
R5C9 is the only square in row 5 that can be <6>
R7C4 is the only square in row 7 that can be <2>
R5C5 is the only square in row 5 that can be <2>
R6C2 is the only square in row 6 that can be <2>
R8C5 is the only square in row 8 that can be <6>
R9C1 is the only square in row 9 that can be <8>
R8C7 is the only square in row 8 that can be <8>
R9C6 is the only square in row 9 that can be <3>
R5C4 is the only square in column 4 that can be <3>
Squares R4C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <7> from <147> leaving <14>
R2C5 - removing <57> from <14579> leaving <149>
R6C5 - removing <5> from <459> leaving <49>
R1C4 is the only square in row 1 that can be <7>
Intersection of column 2 with block 7. The value <5> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <5> from <1345> leaving <134>
Intersection of block 2 with column 4. The value <5> only appears in one or more of squares R1C4, R2C4 and R3C4 of block 2. These squares are the ones that intersect with column 4. Thus, the other (non-intersecting) squares of column 4 cannot contain this value.
R8C4 - removing <5> from <459> leaving <49>
Squares R1C8<14>, R3C7<15> and R3C8<145> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <145> from <12345> leaving <23>
R2C9 - removing <5> from <235> leaving <23>
R2C4 is the only square in row 2 that can be <5>
Squares R2C8, R2C9, R4C8 and R4C9 form a Type-3 Unique Rectangle on <23>. Upon close inspection, it is clear that:
(R4C8 or R4C9)<57> and R5C7<57> form a naked pair on <57> in block 6. No other squares in the block can contain these possibilities
R6C7 - removing <5> from <35> leaving <3>
(R4C8 or R4C9)<57> and R4C5<57> form a naked pair on <57> in row 4. No other squares in the row can contain these possibilities
R4C3 - removing <5> from <35> leaving <3>
R6C1 can only be <4>
R6C5 can only be <9>
R5C1 can only be <1>
R6C6 can only be <5>
R4C5 can only be <7>
R9C5 can only be <5>
R5C6 can only be <4>
R5C3 can only be <5>
R2C1 can only be <7>
R5C7 can only be <7>
R7C6 can only be <7>
R8C6 can only be <9>
R8C4 can only be <4>
R9C2 can only be <7>
R8C1 can only be <3>
R8C9 can only be <5>
R3C4 can only be <9>
R4C9 can only be <2>
R7C7 can only be <1>
R8C2 can only be <1>
R4C8 can only be <5>
R2C9 can only be <3>
R7C3 can only be <4>
R7C8 can only be <3>
R3C7 can only be <5>
R8C8 can only be <7>
R2C8 can only be <2>
R3C2 can only be <4>
R2C2 can only be <9>
R7C2 can only be <5>
R2C3 can only be <1>
R3C8 can only be <1>
R1C8 can only be <4>
R1C5 can only be <1>
R2C5 can only be <4>
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