Aug 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R5C8 is the only square in row 5 that can be <3>
R7C5 is the only square in row 7 that can be <4>
R2C5 can only be <9>
R3C5 can only be <6>
R2C6 can only be <2>
R3C3 can only be <2>
R8C5 can only be <5>
R1C6 can only be <1>
R9C6 can only be <6>
R8C6 can only be <9>
R9C2 is the only square in row 9 that can be <3>
R1C3 is the only square in column 3 that can be <6>
Intersection of column 7 with block 3. The value <4> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <4> from <459> leaving <59>
R2C8 - removing <4> from <457> leaving <57>
Squares R5C3 and R9C3 in column 3 and R5C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <7> from <278> leaving <28>
R9C8 - removing <7> from <1257> leaving <125>
Squares R1C2<458>, R2C2<458>, R4C2<24> and R5C2<28> in column 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C2 - removing <4> from <467> leaving <67>
R8C2 - removing <28> from <2678> leaving <67>
Intersection of column 2 with block 4. The value <2> 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 this value.
R4C1 - removing <2> from <124> leaving <14>
Squares R8C4, R9C4, R8C8 and R9C8 form a Type-3 Unique Rectangle on <12>. Upon close inspection, it is clear that:
(R8C8 or R9C8)<57> and R2C8<57> form a naked pair on <57> in column 8. No other squares in the column can contain these possibilities
R1C8 - removing <5> from <59> leaving <9>
R6C8 - removing <7> from <147> leaving <14>
(R8C8 or R9C8)<57>, R2C8<57> and R1C8<59> form a naked triplet on <579> in column 8. No other squares in the column can contain these possibilities
R4C8 - removing <9> from <1249> leaving <124>
R1C7 can only be <4>
R1C4 can only be <8>
R3C7 can only be <1>
R3C9 can only be <3>
R3C1 can only be <4>
R1C2 can only be <5>
R2C4 can only be <4>
R4C1 can only be <1>
R4C9 can only be <9>
R6C1 can only be <6>
R6C2 can only be <7>
R6C9 can only be <1>
R8C2 can only be <6>
R5C3 can only be <8>
R6C8 can only be <4>
R2C2 can only be <8>
R2C1 can only be <3>
R5C2 can only be <2>
R5C7 can only be <7>
R4C2 can only be <4>
R7C3 can only be <5>
R9C7 can only be <2>
R4C8 can only be <2>
R7C9 can only be <8>
R9C3 can only be <7>
R7C1 can only be <2>
R8C9 can only be <7>
R2C9 can only be <5>
R9C4 can only be <1>
R7C7 can only be <9>
R8C8 can only be <1>
R2C8 can only be <7>
R8C1 can only be <8>
R8C4 can only be <2>
R9C8 can only be <5>
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