Oct 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 is the only square in row 2 that can be <2>
R5C8 is the only square in row 5 that can be <1>
R5C2 is the only square in row 5 that can be <2>
R6C8 is the only square in row 6 that can be <2>
R6C9 is the only square in row 6 that can be <5>
R2C7 is the only square in row 2 that can be <5>
R8C6 is the only square in row 8 that can be <2>
R9C2 is the only square in row 9 that can be <5>
R7C5 is the only square in row 7 that can be <5>
R7C2 is the only square in row 7 that can be <1>
R7C8 is the only square in row 7 that can be <9>
R5C4 is the only square in column 4 that can be <6>
R5C7 is the only square in column 7 that can be <8>
R5C3 can only be <3>
R6C5 is the only square in row 6 that can be <3>
R3C8 is the only square in row 3 that can be <3>
R9C9 is the only square in row 9 that can be <3>
R9C4 is the only square in row 9 that can be <1>
R2C5 is the only square in row 2 that can be <1>
R8C9 is the only square in row 8 that can be <1>
R4C5 is the only square in block 5 that can be <7>
Squares R4C8 and R4C9 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <6> from <689> leaving <89>
R4C2 - removing <6> from <689> leaving <89>
Intersection of column 3 with block 7. The value <6> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <6> from <4678> leaving <478>
Squares R1C4<379>, R2C4<379> and R2C6<79> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C6 - removing <79> from <4789> leaving <48>
R3C5 - removing <9> from <489> leaving <48>
R3C2 is the only square in row 3 that can be <9>
R4C2 can only be <8>
R4C1 can only be <9>
Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
R8C3 - removing <7> from <678> leaving <68>
R8C7 - removing <7> from <467> leaving <46>
Squares R1C1 and R1C6 in row 1 and R9C1 and R9C6 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 6 can be removed.
R8C1 - removing <8> from <478> leaving <47>
Squares R6C1, R6C2, R1C1 and R1C2 form a Type-1 Unique Rectangle on <67>.
R1C1 - removing <67> from <3678> leaving <38>
Squares R8C1 (XY), R8C7 (XZ) and R7C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R7C7 - removing <6> from <67> leaving <7>
R8C3 - removing <6> from <68> leaving <8>
R7C3 can only be <6>
R3C7 can only be <4>
R9C8 can only be <4>
R8C5 can only be <9>
R3C3 can only be <7>
R8C4 can only be <7>
R5C5 can only be <4>
R9C1 can only be <7>
R4C8 can only be <6>
R8C7 can only be <6>
R1C2 can only be <6>
R3C5 can only be <8>
R4C9 can only be <4>
R1C8 can only be <7>
R5C6 can only be <9>
R2C6 can only be <7>
R8C1 can only be <4>
R9C6 can only be <8>
R6C1 can only be <6>
R1C6 can only be <4>
R1C9 can only be <9>
R6C2 can only be <7>
R2C1 can only be <3>
R1C4 can only be <3>
R2C9 can only be <6>
R2C4 can only be <9>
R1C1 can only be <8>
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