Aug 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <1>
R5C5 can only be <6>
R6C3 can only be <7>
R7C4 can only be <4>
R8C4 can only be <7>
R4C7 can only be <8>
R6C2 can only be <5>
R3C4 can only be <1>
R2C4 can only be <3>
R6C7 can only be <2>
R6C8 can only be <9>
R1C9 is the only square in row 1 that can be <3>
R8C1 is the only square in row 8 that can be <9>
R2C6 is the only square in row 2 that can be <9>
R3C2 is the only square in row 3 that can be <9>
R1C2 is the only square in column 2 that can be <7>
R2C7 is the only square in column 7 that can be <7>
R2C9 is the only square in row 2 that can be <1>
R8C7 is the only square in row 8 that can be <1>
Intersection of row 2 with block 1. The value <6> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C3 - removing <6> from <468> leaving <48>
Squares R4C2, R4C3, R7C2 and R7C3 form a Type-4 Unique Rectangle on <36>.
R7C2 - removing <6> from <368> leaving <38>
R7C3 - removing <6> from <2368> leaving <238>
Squares R5C1, R5C2, R9C1 and R9C2 form a Type-2 Unique Rectangle on <18>.
R8C3 - removing <6> from <268> leaving <28>
R9C8 - removing <6> from <267> leaving <27>
R8C6 is the only square in row 8 that can be <6>
Squares R7C2<38>, R7C3<238> and R8C3<28> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <238>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C1 - removing <8> from <168> leaving <16>
R9C2 - removing <8> from <168> leaving <16>
Squares R3C6 and R7C6 in column 6 and R3C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 3 and 7 can be removed.
R3C8 - removing <5> from <456> leaving <46>
R7C8 - removing <5> from <256> leaving <26>
Squares R1C1 (XY), R1C8 (XZ) and R3C3 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C8 - removing <4> from <46> leaving <6>
R3C7 can only be <5>
R7C8 can only be <2>
R9C8 can only be <7>
R9C9 can only be <8>
R5C8 can only be <5>
R9C5 can only be <2>
R8C9 can only be <5>
R3C6 can only be <8>
R7C7 can only be <6>
R1C8 can only be <4>
R5C9 can only be <7>
R8C5 can only be <8>
R3C3 can only be <4>
R7C6 can only be <5>
R1C5 can only be <5>
R8C3 can only be <2>
R1C1 can only be <8>
R2C5 can only be <4>
R2C3 can only be <6>
R5C1 can only be <1>
R2C1 can only be <5>
R4C3 can only be <3>
R4C2 can only be <6>
R7C3 can only be <8>
R5C2 can only be <8>
R9C1 can only be <6>
R7C2 can only be <3>
R9C2 can only be <1>
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