Nov 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C8 can only be <6>
R6C5 can only be <4>
R6C7 can only be <2>
R6C3 can only be <6>
R1C9 is the only square in row 1 that can be <2>
R3C2 is the only square in row 3 that can be <2>
R7C9 is the only square in row 7 that can be <8>
R8C8 is the only square in row 8 that can be <2>
R8C3 is the only square in row 8 that can be <8>
Squares R2C5 and R3C4 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C5 - removing <67> from <1678> leaving <18>
R3C6 - removing <7> from <178> leaving <18>
Intersection of row 7 with block 7. The values <34> 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 these values.
R9C1 - removing <4> from <456> leaving <56>
R9C3 - removing <4> from <457> leaving <57>
Squares R8C2<67>, R9C1<56> and R9C3<57> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <6> from <346> leaving <34>
R7C2 - removing <67> from <3467> leaving <34>
Squares R5C2 and R7C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <4> from <467> leaving <67>
Squares R2C2 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <7> from <457> leaving <45>
R2C7 - removing <67> from <4679> leaving <49>
R2C8 - removing <7> from <579> leaving <59>
Intersection of row 7 with block 8. The values <16> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C5 - removing <6> from <679> leaving <79>
Squares R1C1<36>, R1C3<37> and R2C2<67> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <367>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C1 - removing <6> from <456> leaving <45>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
R8C7 - removing <7> from <679> leaving <69>
Squares R2C2 and R2C5 in row 2 and R8C2 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 5 can be removed.
R5C5 - removing <7> from <3789> leaving <389>
R7C5 - removing <7> from <1679> leaving <169>
Squares R2C7 (XY), R3C9 (XZ) and R8C7 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R1C7 - removing <6> from <67> leaving <7>
R9C9 - removing <6> from <46> leaving <4>
R1C3 can only be <3>
R3C8 can only be <5>
R3C1 can only be <4>
R2C8 can only be <9>
R9C7 can only be <6>
R3C9 can only be <6>
R1C1 can only be <6>
R4C3 can only be <1>
R2C7 can only be <4>
R7C8 can only be <7>
R7C1 can only be <3>
R2C3 can only be <5>
R3C4 can only be <7>
R4C7 can only be <8>
R5C3 can only be <4>
R4C5 can only be <3>
R5C7 can only be <1>
R5C2 can only be <3>
R7C2 can only be <4>
R7C6 can only be <1>
R9C1 can only be <5>
R8C7 can only be <9>
R2C2 can only be <7>
R2C5 can only be <6>
R8C2 can only be <6>
R9C3 can only be <7>
R5C4 can only be <9>
R5C5 can only be <8>
R7C4 can only be <6>
R5C6 can only be <7>
R3C5 can only be <1>
R7C5 can only be <9>
R3C6 can only be <8>
R8C5 can only be <7>
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