Apr 03 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <1>
R1C6 can only be <5>
R4C5 can only be <1>
R6C1 can only be <1>
R5C4 can only be <3>
R1C5 can only be <2>
R6C5 can only be <5>
R9C4 can only be <9>
R6C9 can only be <4>
R2C5 can only be <8>
R3C8 is the only square in row 3 that can be <5>
R7C7 is the only square in row 7 that can be <3>
R9C5 is the only square in row 9 that can be <3>
Intersection of column 7 with block 3. The values <24> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R3C9 - removing <2> from <126> leaving <16>
Squares R7C8<19>, R8C7<69> and R9C7<16> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <169>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <169> from <16789> leaving <78>
R9C9 - removing <16> from <1678> leaving <78>
Intersection of row 7 with block 7. The value <6> 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.
R8C3 - removing <6> from <679> leaving <79>
R9C1 - removing <6> from <2678> leaving <278>
R9C3 - removing <6> from <12678> leaving <1278>
Intersection of column 9 with block 3. The value <6> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <6> from <469> leaving <49>
R3C7 - removing <6> from <1246> leaving <124>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C3 - removing <9> from <679> leaving <67>
R1C7 - removing <9> from <49> leaving <4>
R7C3 - removing <9> from <16789> leaving <1678>
R3C1 is the only square in row 3 that can be <4>
Squares R1C1 and R1C9 in row 1 and R4C1 and R4C9 in row 4 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.
R5C1 - removing <9> from <289> leaving <28>
R5C9 - removing <9> from <129> leaving <12>
R7C1 - removing <9> from <6789> leaving <678>
Squares R3C2 (XY), R2C3 (XZ) and R7C2 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R8C3 - removing <9> from <79> leaving <7>
R8C5 can only be <6>
R1C3 can only be <6>
R8C7 can only be <9>
R5C5 can only be <7>
R9C6 can only be <7>
R2C7 can only be <2>
R7C8 can only be <1>
R9C9 can only be <8>
R5C6 can only be <6>
R9C1 can only be <2>
R7C9 can only be <7>
R1C9 can only be <9>
R1C1 can only be <7>
R4C9 can only be <2>
R2C3 can only be <9>
R3C7 can only be <1>
R3C9 can only be <6>
R9C7 can only be <6>
R4C1 can only be <9>
R5C9 can only be <1>
R5C8 can only be <9>
R7C3 can only be <8>
R9C3 can only be <1>
R5C1 can only be <8>
R5C2 can only be <2>
R7C1 can only be <6>
R3C2 can only be <8>
R7C2 can only be <9>
R3C3 can only be <2>
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