Jul 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C1 can only be <3>
R5C9 can only be <2>
R6C5 can only be <2>
R5C2 can only be <7>
R5C4 can only be <6>
R5C6 can only be <5>
R4C8 can only be <9>
R6C8 can only be <3>
R6C2 can only be <8>
R4C5 can only be <7>
R5C8 can only be <1>
R5C5 can only be <9>
R4C2 can only be <2>
R3C3 is the only square in row 3 that can be <8>
R2C5 is the only square in row 2 that can be <8>
R8C8 is the only square in row 8 that can be <8>
R8C7 is the only square in row 8 that can be <7>
R2C8 is the only square in row 2 that can be <7>
Intersection of row 3 with block 3. The value <2> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <2> from <124> leaving <14>
Intersection of row 7 with block 7. The value <1> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C2 - removing <1> from <134569> leaving <34569>
R8C3 - removing <1> from <136> leaving <36>
Squares R2C4<12>, R2C6<24> and R2C7<14> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C2 - removing <1> from <13569> leaving <3569>
R2C3 - removing <1> from <136> leaving <36>
R7C3 is the only square in column 3 that can be <1>
Squares R3C2 and R3C8 in row 3 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <5> from <3569> leaving <369>
R8C2 - removing <5> from <34569> leaving <3469>
Squares R1C2 and R1C8 in row 1 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <6> from <369> leaving <39>
R8C2 - removing <6> from <3469> leaving <349>
Squares R1C8 (XY), R9C8 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R8C9 - removing <5> from <56> leaving <6>
R3C8 - removing <5> from <25> leaving <2>
R3C7 can only be <1>
R8C3 can only be <3>
R2C9 can only be <5>
R7C8 can only be <4>
R2C1 can only be <9>
R3C2 can only be <5>
R2C7 can only be <4>
R7C2 can only be <6>
R7C7 can only be <2>
R1C8 can only be <6>
R9C8 can only be <5>
R2C3 can only be <6>
R9C2 can only be <4>
R1C2 can only be <1>
R2C2 can only be <3>
R8C1 can only be <5>
R2C6 can only be <2>
R9C5 can only be <3>
R8C2 can only be <9>
R1C5 can only be <4>
R8C5 can only be <1>
R2C4 can only be <1>
R8C6 can only be <4>
R8C4 can only be <2>
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