Jun 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C6 is the only square in row 5 that can be <1>
R8C4 is the only square in column 4 that can be <3>
R4C6 is the only square in column 6 that can be <7>
Squares R5C3 and R5C7 in row 5 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.
R5C1 - removing <46> from <24679> leaving <279>
R5C2 - removing <4> from <2479> leaving <279>
R5C4 - removing <6> from <2568> leaving <258>
R5C8 - removing <46> from <4568> leaving <58>
R5C9 - removing <46> from <45689> leaving <589>
Intersection of column 4 with block 5. The values <56> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <6> from <2469> leaving <249>
R6C5 - removing <56> from <45689> leaving <489>
R6C6 - removing <6> from <46> leaving <4>
R2C6 can only be <2>
R2C4 can only be <8>
R8C6 can only be <6>
R2C5 can only be <4>
R6C5 is the only square in column 5 that can be <8>
R4C5 is the only square in column 5 that can be <9>
Squares R4C9 and R5C7 in block 6 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.
R6C9 - removing <6> from <569> leaving <59>
Squares R1C3<14>, R2C1<17> and R3C2<47> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <147>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <14> from <13458> leaving <358>
R1C2 - removing <4> from <34> leaving <3>
R3C1 - removing <47> from <4578> leaving <58>
Squares R4C1 and R4C9 in row 4 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C9 - removing <4> from <12468> leaving <1268>
R3C9 - removing <4> from <4678> leaving <678>
R7C1 - removing <4> from <2346> leaving <236>
R7C9 - removing <4> from <23467> leaving <2367>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C8 - removing <4> from <468> leaving <68>
Squares R1C1<58>, R1C5<56> and R1C8<68> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C7 - removing <6> from <246> leaving <24>
R1C9 - removing <68> from <1268> leaving <12>
Squares R5C3 and R9C3 in column 3 and R5C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 5 and 9 can be removed.
R9C1 - removing <6> from <12369> leaving <1239>
R9C8 - removing <6> from <567> leaving <57>
R9C9 - removing <6> from <23567> leaving <2357>
Squares R8C9 (XY), R9C7 (XZ) and R4C9 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R7C9 - removing <6> from <2367> leaving <237>
R5C7 - removing <6> from <46> leaving <4>
R5C3 can only be <6>
R1C7 can only be <2>
R4C9 can only be <6>
R1C9 can only be <1>
R9C7 can only be <6>
R1C3 can only be <4>
R2C9 can only be <7>
R2C1 can only be <1>
R4C4 can only be <2>
R3C9 can only be <8>
R9C3 can only be <1>
R6C1 can only be <9>
R6C9 can only be <5>
R6C4 can only be <6>
R5C8 can only be <8>
R3C2 can only be <7>
R5C2 can only be <2>
R3C1 can only be <5>
R5C9 can only be <9>
R1C8 can only be <6>
R4C1 can only be <4>
R5C4 can only be <5>
R5C1 can only be <7>
R7C2 can only be <4>
R9C2 can only be <9>
R7C8 can only be <7>
R8C1 can only be <2>
R7C5 can only be <2>
R9C8 can only be <5>
R8C5 can only be <1>
R8C9 can only be <4>
R9C1 can only be <3>
R9C9 can only be <2>
R7C1 can only be <6>
R9C5 can only be <7>
R7C9 can only be <3>
R1C5 can only be <5>
R3C8 can only be <4>
R3C5 can only be <6>
R1C1 can only be <8>
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