Aug 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C2 can only be <6>
R1C5 is the only square in row 1 that can be <1>
R1C1 is the only square in row 1 that can be <7>
R3C8 is the only square in row 3 that can be <9>
R3C9 is the only square in row 3 that can be <5>
R1C9 can only be <6>
R2C9 can only be <8>
R1C3 is the only square in row 1 that can be <5>
R9C1 is the only square in column 1 that can be <4>
R1C7 is the only square in column 7 that can be <2>
R6C3 is the only square in block 4 that can be <1>
R9C3 can only be <6>
R2C3 can only be <3>
R2C8 can only be <4>
R7C3 can only be <9>
R3C2 can only be <8>
R2C4 can only be <6>
R1C8 can only be <3>
R3C1 can only be <6>
R1C6 can only be <4>
R3C4 can only be <2>
R3C6 can only be <3>
R7C1 is the only square in column 1 that can be <8>
R7C5 can only be <6>
R7C7 can only be <3>
R8C2 is the only square in row 8 that can be <3>
Squares R8C6<78>, R9C5<28> and R9C6<278> in block 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <278>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <7> from <157> leaving <15>
R7C6 - removing <7> from <57> leaving <5>
R8C4 - removing <7> from <1479> leaving <149>
R8C5 - removing <8> from <489> leaving <49>
R7C4 can only be <1>
R7C2 can only be <7>
R9C2 can only be <1>
Intersection of column 4 with block 5. The values <57> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C6 - removing <7> from <267> leaving <26>
R6C6 - removing <7> from <678> leaving <68>
Squares R4C1<239>, R4C5<239>, R4C6<26> and R4C7<69> in row 4 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C4 - removing <9> from <579> leaving <57>
R4C8 - removing <6> from <1567> leaving <157>
Squares R8C4, R8C5, R6C4 and R6C5 form a Type-4 Unique Rectangle on <49>.
R6C4 - removing <9> from <479> leaving <47>
R6C5 - removing <9> from <3489> leaving <348>
Squares R4C9, R8C9, R4C8 and R8C8 form a Type-4 Unique Rectangle on <17>.
R4C8 - removing <7> from <157> leaving <15>
R8C8 - removing <7> from <1678> leaving <168>
Squares R6C7 (XYZ), R6C6 (XZ) and R4C7 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R6C8 - removing <6> from <678> leaving <78>
R8C8 is the only square in column 8 that can be <6>
R8C7 can only be <8>
R8C6 can only be <7>
R9C8 can only be <7>
R6C8 can only be <8>
R8C9 can only be <1>
R6C6 can only be <6>
R5C8 can only be <5>
R4C9 can only be <7>
R4C4 can only be <5>
R5C4 can only be <9>
R4C8 can only be <1>
R6C7 can only be <9>
R4C6 can only be <2>
R6C1 can only be <3>
R4C7 can only be <6>
R9C6 can only be <8>
R5C1 can only be <2>
R5C5 can only be <8>
R8C4 can only be <4>
R4C5 can only be <3>
R9C5 can only be <2>
R6C5 can only be <4>
R4C1 can only be <9>
R6C4 can only be <7>
R8C5 can only be <9>
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