Oct 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <5>
R5C5 can only be <1>
R9C2 can only be <1>
R4C3 can only be <4>
R4C2 can only be <7>
R4C8 can only be <2>
R5C1 can only be <3>
R5C3 can only be <5>
R5C7 can only be <8>
R8C1 can only be <4>
R6C2 can only be <8>
R6C3 can only be <1>
R5C2 can only be <6>
R5C9 can only be <7>
R6C7 can only be <3>
R5C8 can only be <4>
R6C8 can only be <9>
R2C1 can only be <7>
R3C8 is the only square in row 3 that can be <7>
R8C6 is the only square in row 8 that can be <7>
Squares R8C4 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C5 - removing <6> from <5689> leaving <589>
R8C8 - removing <16> from <13568> leaving <358>
Intersection of row 3 with block 2. The value <1> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C4 - removing <1> from <1346> leaving <346>
R2C6 - removing <1> from <159> leaving <59>
Squares R1C2 and R1C8 in row 1 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <3> from <2345> leaving <245>
R2C8 - removing <3> from <1368> leaving <168>
R3C2 - removing <3> from <235> leaving <25>
R8C2 - removing <3> from <239> leaving <29>
R8C8 - removing <3> from <358> leaving <58>
R3C4 is the only square in row 3 that can be <3>
R3C6 is the only square in row 3 that can be <1>
Squares R1C5 and R2C4 in block 2 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 block.
R2C5 - removing <46> from <24569> leaving <259>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 8 can be removed.
R2C8 - removing <6> from <168> leaving <18>
Squares R1C8 (XY), R2C9 (XZ) and R9C8 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R2C8 - removing <8> from <18> leaving <1>
R8C9 - removing <8> from <38> leaving <3>
R2C7 can only be <6>
R8C3 can only be <2>
R2C9 can only be <8>
R7C8 can only be <5>
R2C4 can only be <4>
R8C7 can only be <1>
R1C8 can only be <3>
R7C6 can only be <9>
R8C8 can only be <8>
R8C2 can only be <9>
R2C3 can only be <3>
R8C4 can only be <6>
R9C8 can only be <6>
R9C5 can only be <8>
R1C2 can only be <4>
R7C4 can only be <1>
R1C5 can only be <6>
R7C2 can only be <3>
R7C5 can only be <4>
R2C6 can only be <5>
R8C5 can only be <5>
R3C5 can only be <2>
R2C2 can only be <2>
R3C2 can only be <5>
R2C5 can only be <9>
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