Jul 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <9>
R4C3 can only be <2>
R4C1 can only be <5>
R4C7 can only be <7>
R4C9 can only be <8>
R6C7 is the only square in row 6 that can be <2>
R1C7 can only be <4>
R5C7 can only be <9>
R9C7 can only be <5>
R2C7 can only be <6>
R8C7 can only be <1>
R6C3 is the only square in row 6 that can be <9>
R8C5 is the only square in row 8 that can be <5>
R2C4 is the only square in column 4 that can be <9>
R6C5 is the only square in column 5 that can be <6>
R6C1 can only be <3>
R6C9 can only be <4>
R3C1 can only be <6>
R5C8 can only be <3>
Intersection of block 8 with row 8. The value <7> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C1 - removing <7> from <247> leaving <24>
R8C3 - removing <7> from <3678> leaving <368>
R8C8 - removing <7> from <4789> leaving <489>
R8C9 - removing <7> from <679> leaving <69>
Squares R1C3 and R1C8 in row 1 and R9C3 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 8 can be removed.
R2C3 - removing <7> from <1378> leaving <138>
R2C8 - removing <7> from <257> leaving <25>
R7C8 - removing <7> from <478> leaving <48>
Squares R5C4, R5C6, R8C4 and R8C6 form a Type-1 Unique Rectangle on <47>.
R8C6 - removing <47> from <347> leaving <3>
R2C6 can only be <4>
R9C5 can only be <4>
R8C4 can only be <7>
R5C6 can only be <7>
R5C4 can only be <4>
Squares R7C2 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C2 - removing <68> from <2689> leaving <29>
Squares R7C9<67>, R8C9<69> and R9C8<79> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <9> from <489> leaving <48>
Squares R3C2 (XY), R9C2 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R9C8 - removing <9> from <79> leaving <7>
R9C3 can only be <3>
R1C8 can only be <2>
R7C9 can only be <6>
R2C8 can only be <5>
R3C8 can only be <9>
R3C9 can only be <3>
R3C2 can only be <5>
R2C9 can only be <7>
R7C2 can only be <8>
R8C9 can only be <9>
R8C2 can only be <2>
R9C2 can only be <9>
R2C1 can only be <2>
R7C8 can only be <4>
R1C2 can only be <3>
R8C3 can only be <6>
R7C1 can only be <7>
R8C8 can only be <8>
R8C1 can only be <4>
R5C3 can only be <1>
R1C5 can only be <8>
R2C2 can only be <1>
R1C3 can only be <7>
R2C5 can only be <3>
R2C3 can only be <8>
R5C2 can only be <6>
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