Dec 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 is the only square in row 2 that can be <6>
R1C7 is the only square in row 1 that can be <6>
R5C5 is the only square in row 5 that can be <6>
R5C4 is the only square in row 5 that can be <8>
R6C3 is the only square in row 6 that can be <3>
R4C7 is the only square in row 4 that can be <3>
R3C9 is the only square in row 3 that can be <3>
R1C9 can only be <1>
R2C9 can only be <7>
R1C4 is the only square in row 1 that can be <3>
R3C5 is the only square in row 3 that can be <7>
R3C1 is the only square in row 3 that can be <1>
R2C1 can only be <4>
R2C4 can only be <1>
R3C2 can only be <2>
R7C4 can only be <2>
R1C1 can only be <9>
R8C4 can only be <4>
R6C4 can only be <7>
R1C3 can only be <8>
R4C4 can only be <9>
R7C1 is the only square in row 7 that can be <3>
R7C7 is the only square in row 7 that can be <5>
R5C9 is the only square in column 9 that can be <5>
R8C1 is the only square in column 1 that can be <5>
R6C2 is the only square in column 2 that can be <5>
Squares R8C9 and R9C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <2> from <268> leaving <68>
Intersection of row 5 with block 4. The values <29> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C3 - removing <2> from <247> leaving <47>
Intersection of row 8 with block 9. The value <8> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <8> from <178> leaving <17>
Squares R4C3 and R4C8 in row 4 and R7C3 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 8 can be removed.
R5C3 - removing <7> from <2479> leaving <249>
R9C3 - removing <7> from <12479> leaving <1249>
Squares R8C9, R9C9, R8C3 and R9C3 form a Type-3 Unique Rectangle on <29>. Upon close inspection, it is clear that:
(R8C3 or R9C3)<14>, R7C3<17> and R4C3<47> form a naked triplet on <147> in column 3. No other squares in the column can contain these possibilities
R5C3 - removing <4> from <249> leaving <29>
Squares R7C8 (XY), R7C6 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C5 - removing <1> from <18> leaving <8>
R9C6 - removing <1> from <168> leaving <68>
R9C6 can only be <6>
R2C5 can only be <5>
R7C6 can only be <1>
R2C6 can only be <8>
R7C3 can only be <7>
R7C8 can only be <6>
R4C3 can only be <4>
R9C1 can only be <2>
R8C8 can only be <8>
R8C7 can only be <1>
R3C8 can only be <4>
R9C9 can only be <9>
R5C1 can only be <7>
R9C2 can only be <4>
R8C9 can only be <2>
R3C7 can only be <8>
R6C8 can only be <2>
R4C5 can only be <2>
R9C3 can only be <1>
R5C2 can only be <9>
R4C6 can only be <5>
R4C8 can only be <7>
R1C5 can only be <4>
R6C6 can only be <4>
R5C7 can only be <4>
R5C3 can only be <2>
R8C2 can only be <6>
R6C5 can only be <1>
R1C6 can only be <2>
R8C3 can only be <9>
R9C7 can only be <7>
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