Oct 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <1>
R4C1 is the only square in row 4 that can be <4>
R6C7 is the only square in row 6 that can be <5>
R8C7 can only be <4>
R8C2 can only be <7>
R8C3 can only be <1>
R8C5 can only be <2>
R8C8 can only be <5>
R2C3 is the only square in row 2 that can be <2>
R3C4 is the only square in row 3 that can be <2>
R4C9 is the only square in row 4 that can be <2>
R5C2 is the only square in row 5 that can be <5>
R6C6 is the only square in row 6 that can be <1>
R5C7 is the only square in row 5 that can be <1>
R6C1 is the only square in row 6 that can be <2>
R7C5 is the only square in row 7 that can be <1>
R7C8 is the only square in row 7 that can be <2>
R7C2 is the only square in column 2 that can be <4>
R3C3 is the only square in column 3 that can be <3>
R1C1 is the only square in block 1 that can be <7>
Intersection of row 1 with block 2. The values <356> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R2C5 - removing <36> from <3678> leaving <78>
R3C5 - removing <6> from <4678> leaving <478>
Squares R1C6<35>, R4C6<38> and R7C6<58> in column 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <358>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <8> from <478> leaving <47>
R9C6 - removing <3> from <347> leaving <47>
Intersection of block 2 with column 5. The value <8> only appears in one or more of squares R1C5, R2C5 and R3C5 of block 2. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R5C5 - removing <8> from <3678> leaving <367>
Squares R4C3 and R4C7 in row 4 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C7 - removing <9> from <679> leaving <67>
R5C3 - removing <9> from <6789> leaving <678>
R3C8 is the only square in row 3 that can be <9>
Squares R3C6, R9C6, R3C5 and R9C5 form a Type-4 Unique Rectangle on <47>.
R3C5 - removing <7> from <478> leaving <48>
R9C5 - removing <7> from <347> leaving <34>
Squares R5C9 (XYZ), R5C1 (XZ) and R6C9 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R5C8 - removing <6> from <36> leaving <3>
R2C8 can only be <6>
R2C2 can only be <8>
R3C7 can only be <7>
R3C6 can only be <4>
R2C7 can only be <3>
R2C5 can only be <7>
R3C2 can only be <6>
R5C5 can only be <6>
R3C5 can only be <8>
R9C6 can only be <7>
R5C1 can only be <9>
R1C5 can only be <3>
R9C4 can only be <3>
R1C6 can only be <5>
R9C5 can only be <4>
R1C4 can only be <6>
R7C6 can only be <8>
R5C9 can only be <8>
R9C1 can only be <6>
R5C3 can only be <7>
R6C9 can only be <6>
R9C9 can only be <9>
R4C7 can only be <9>
R7C4 can only be <5>
R4C6 can only be <3>
R7C3 can only be <9>
R4C4 can only be <8>
R7C7 can only be <6>
R4C3 can only be <6>
R6C4 can only be <7>
R6C3 can only be <8>
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