Oct 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <8>
R5C9 can only be <2>
R3C4 can only be <6>
R7C6 can only be <2>
R2C5 can only be <9>
R5C6 can only be <4>
R3C7 can only be <1>
R1C5 can only be <4>
R3C9 can only be <7>
R1C9 can only be <6>
R4C4 is the only square in row 4 that can be <2>
R5C5 is the only square in row 5 that can be <6>
R5C1 is the only square in row 5 that can be <3>
R3C1 can only be <5>
R3C3 can only be <3>
R6C5 is the only square in row 6 that can be <3>
R7C7 is the only square in row 7 that can be <6>
Squares R7C9 and R9C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C7 - removing <9> from <259> leaving <25>
Intersection of column 5 with block 8. The value <1> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <1> from <158> leaving <58>
Squares R2C2 and R5C2 in column 2 and R2C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 5 can be removed.
R5C4 - removing <8> from <158> leaving <15>
Squares R7C9, R9C9, R7C1 and R9C1 form a Type-2 Unique Rectangle on <19>.
R1C1 - removing <8> from <18> leaving <1>
R7C3 - removing <8> from <158> leaving <15>
R9C3 - removing <8> from <1258> leaving <125>
Squares R5C4 (XY), R5C2 (XZ) and R4C5 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R4C3 - removing <8> from <78> leaving <7>
R4C6 can only be <9>
R6C6 can only be <7>
R6C7 is the only square in row 6 that can be <9>
Squares R7C3 (XY), R6C3 (XZ) and R7C4 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R6C4 - removing <8> from <18> leaving <1>
R6C3 can only be <8>
R5C4 can only be <5>
R5C8 can only be <8>
R7C4 can only be <8>
R4C5 can only be <8>
R5C2 can only be <1>
R2C8 can only be <2>
R4C7 can only be <5>
R1C3 can only be <2>
R7C1 can only be <9>
R1C7 can only be <8>
R2C2 can only be <8>
R8C8 can only be <5>
R9C7 can only be <2>
R8C2 can only be <2>
R7C9 can only be <1>
R9C1 can only be <8>
R7C3 can only be <5>
R9C9 can only be <9>
R8C5 can only be <1>
R9C3 can only be <1>
R9C5 can only be <5>
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