Jun 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <7>
R2C4 can only be <5>
R3C5 can only be <6>
R4C5 can only be <2>
R8C6 can only be <7>
R4C8 can only be <7>
R5C4 can only be <3>
R4C2 can only be <5>
R5C7 can only be <2>
R8C4 can only be <2>
R6C5 can only be <1>
R5C8 can only be <4>
R6C8 can only be <3>
R6C2 can only be <2>
R2C5 can only be <7>
R5C5 can only be <8>
R5C6 can only be <5>
R2C6 can only be <1>
R7C5 can only be <4>
R8C5 can only be <3>
Squares R1C1<15>, R1C2<16>, R2C3<69> and R3C3<59> in block 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1569>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C2 - removing <69> from <34689> leaving <348>
R3C2 - removing <9> from <389> leaving <38>
Intersection of column 2 with block 7. The value <9> 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 <9> from <579> leaving <57>
R8C3 - removing <9> from <1569> leaving <156>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C8 - removing <6> from <2689> leaving <289>
R8C2 - removing <6> from <14689> leaving <1489>
R8C8 - removing <6> from <15689> leaving <1589>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <8> from <348> leaving <34>
R2C8 - removing <8> from <289> leaving <29>
R8C2 - removing <8> from <1489> leaving <149>
R8C8 - removing <8> from <1589> leaving <159>
Squares R2C9 (XY), R9C9 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R9C1 - removing <4> from <14> leaving <1>
R1C1 can only be <5>
R1C8 can only be <6>
R3C3 can only be <9>
R1C2 can only be <1>
R9C8 can only be <2>
R2C3 can only be <6>
R9C9 can only be <4>
R2C8 can only be <9>
R9C2 can only be <6>
R8C9 can only be <8>
R5C2 can only be <7>
R8C3 can only be <5>
R2C7 can only be <3>
R5C3 can only be <1>
R8C8 can only be <1>
R7C3 can only be <7>
R8C1 can only be <4>
R2C9 can only be <2>
R7C8 can only be <5>
R2C2 can only be <4>
R3C7 can only be <5>
R3C8 can only be <8>
R7C7 can only be <9>
R3C2 can only be <3>
R7C2 can only be <8>
R8C7 can only be <6>
R8C2 can only be <9>
R2C1 can only be <8>
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