Aug 03 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <6>
R2C2 is the only square in row 2 that can be <9>
R8C8 is the only square in row 8 that can be <5>
R3C6 is the only square in column 6 that can be <4>
R3C7 can only be <8>
R2C8 can only be <3>
R1C5 is the only square in row 1 that can be <3>
R5C7 is the only square in row 5 that can be <3>
R9C8 is the only square in column 8 that can be <8>
R1C9 is the only square in column 9 that can be <5>
R3C3 is the only square in block 1 that can be <5>
R3C4 can only be <2>
Squares R7C6 and R7C7 in row 7 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 row.
R7C3 - removing <7> from <178> leaving <18>
Squares R5C1<28>, R5C3<278> and R6C2<27> in block 4 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.
R5C2 - removing <278> from <24578> leaving <45>
Squares R5C3 and R9C3 in column 3 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 5 and 9 can be removed.
R9C2 - removing <7> from <267> leaving <26>
R9C7 - removing <7> from <479> leaving <49>
R5C8 - removing <7> from <1479> leaving <149>
Squares R9C1 and R9C2 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <2> from <127> leaving <17>
R9C5 - removing <26> from <1269> leaving <19>
Squares R9C1 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C2 - removing <26> from <2678> leaving <78>
Squares R9C1, R9C2, R1C1 and R1C2 form a Type-2 Unique Rectangle on <26>.
R1C3 - removing <8> from <28> leaving <2>
Squares R6C5 (XY), R9C5 (XZ) and R5C6 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R5C5 - removing <9> from <12569> leaving <1256>
R7C6 - removing <9> from <79> leaving <7>
R4C5 - removing <9> from <59> leaving <5>
R4C2 can only be <4>
R2C5 can only be <8>
R7C7 can only be <9>
R8C6 can only be <2>
R9C7 can only be <4>
R5C6 can only be <9>
R9C9 can only be <7>
R1C7 can only be <7>
R9C3 can only be <1>
R5C9 can only be <4>
R1C8 can only be <4>
R4C8 can only be <9>
R2C4 can only be <5>
R8C5 can only be <6>
R5C2 can only be <5>
R5C8 can only be <1>
R5C4 can only be <6>
R6C8 can only be <7>
R6C2 can only be <2>
R8C4 can only be <8>
R5C5 can only be <2>
R9C5 can only be <9>
R7C3 can only be <8>
R5C1 can only be <8>
R6C5 can only be <1>
R9C2 can only be <6>
R7C4 can only be <1>
R5C3 can only be <7>
R8C2 can only be <7>
R9C1 can only be <2>
R1C2 can only be <8>
R1C1 can only be <6>
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