Sep 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 can only be <3>
R5C5 can only be <5>
R8C9 can only be <5>
R2C5 can only be <2>
R2C9 can only be <7>
R8C5 can only be <6>
R8C1 can only be <7>
R1C5 is the only square in row 1 that can be <1>
R5C7 is the only square in row 5 that can be <7>
R5C3 is the only square in row 5 that can be <8>
R4C3 is the only square in column 3 that can be <2>
Squares R3C1 and R3C9 in row 3 and R4C1 and R4C9 in row 4 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 9 can be removed.
R5C1 - removing <6> from <469> leaving <49>
R5C9 - removing <6> from <2469> leaving <249>
Squares R5C8 (XY), R9C8 (XZ) and R4C9 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R7C9 - removing <3> from <234> leaving <24>
Intersection of row 7 with block 8. The values <38> 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.
R9C5 - removing <3> from <39> leaving <9>
R9C6 - removing <3> from <357> leaving <57>
Squares R7C4<25>, R9C4<257> and R9C6<57> in block 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C6 - removing <5> from <358> leaving <38>
Squares R5C9<249>, R6C9<49> and R7C9<24> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <249>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <9> from <369> leaving <36>
R3C4 is the only square in row 3 that can be <9>
R1C7 is the only square in row 1 that can be <9>
Squares R7C5, R7C6, R3C5 and R3C6 form a Type-1 Unique Rectangle on <38>.
R3C6 - removing <38> from <358> leaving <5>
R3C1 can only be <6>
R9C6 can only be <7>
R1C4 can only be <7>
R1C6 can only be <3>
R1C8 can only be <6>
R7C6 can only be <8>
R3C5 can only be <8>
R5C8 can only be <2>
R3C9 can only be <3>
R4C1 can only be <1>
R7C5 can only be <3>
R4C9 can only be <6>
R4C7 can only be <3>
R9C7 can only be <4>
R9C8 can only be <3>
R6C7 can only be <1>
R7C9 can only be <2>
R7C4 can only be <5>
R7C1 can only be <4>
R9C4 can only be <2>
R5C1 can only be <9>
R5C9 can only be <4>
R6C1 can only be <5>
R5C2 can only be <6>
R6C9 can only be <9>
R6C3 can only be <4>
R1C3 can only be <5>
R1C2 can only be <4>
R9C3 can only be <6>
R9C2 can only be <5>
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