Jun 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C3 can only be <5>
R5C5 can only be <5>
R4C7 can only be <3>
R4C8 can only be <9>
R4C2 can only be <2>
R1C2 is the only square in row 1 that can be <5>
R3C4 is the only square in row 3 that can be <3>
R6C2 is the only square in row 6 that can be <3>
R6C3 is the only square in row 6 that can be <6>
R9C1 is the only square in row 9 that can be <3>
R9C8 is the only square in row 9 that can be <5>
R6C8 can only be <7>
R6C7 can only be <5>
Intersection of row 3 with block 2. The value <6> 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.
R1C5 - removing <6> from <246> leaving <24>
R2C6 - removing <6> from <2456> leaving <245>
Squares R1C5 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <4> from <467> leaving <67>
Squares R2C6 and R2C7 in row 2 and R8C6 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 6 and 7 can be removed.
R7C6 - removing <2> from <246> leaving <46>
R7C7 - removing <2> from <1247> leaving <147>
Squares R3C6 and R7C6 in column 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 column.
R2C6 - removing <4> from <245> leaving <25>
R8C6 - removing <4> from <245> leaving <25>
Squares R2C1, R2C3 and R2C7 in row 2, R5C1 and R5C3 in row 5 and R8C1, R8C3 and R8C7 in row 8 form a Swordfish pattern on possibility <4>. All other instances of this possibility in columns 1, 3 and 7 can be removed.
R3C3 - removing <4> from <4789> leaving <789>
R3C7 - removing <4> from <1478> leaving <178>
R7C3 - removing <4> from <14789> leaving <1789>
R7C7 - removing <4> from <147> leaving <17>
Squares R7C7<17>, R8C9<179> and R9C9<79> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <179>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <1> from <124> leaving <24>
R8C7 - removing <17> from <1247> leaving <24>
R3C8 is the only square in column 8 that can be <1>
Squares R1C9<67>, R2C9<68> and R3C7<78> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <678>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C7 - removing <8> from <248> leaving <24>
Squares R3C6, R7C6, R3C5 and R7C5 form a Type-4 Unique Rectangle on <46>.
R3C5 - removing <4> from <469> leaving <69>
R7C5 - removing <4> from <2469> leaving <269>
Squares R3C5 (XY), R3C6 (XZ) and R9C5 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R1C5 - removing <4> from <24> leaving <2>
R7C6 - removing <4> from <46> leaving <6>
R1C8 can only be <4>
R2C6 can only be <5>
R7C8 can only be <2>
R2C7 can only be <2>
R2C4 can only be <9>
R8C6 can only be <2>
R8C7 can only be <4>
R7C5 can only be <9>
R3C6 can only be <4>
R7C4 can only be <7>
R3C5 can only be <6>
R7C7 can only be <1>
R8C4 can only be <5>
R9C5 can only be <4>
R7C3 can only be <8>
R5C7 can only be <8>
R9C2 can only be <7>
R5C9 can only be <1>
R3C7 can only be <7>
R7C2 can only be <4>
R2C3 can only be <4>
R9C9 can only be <9>
R3C2 can only be <8>
R8C1 can only be <9>
R8C9 can only be <7>
R2C1 can only be <6>
R5C3 can only be <7>
R3C3 can only be <9>
R1C9 can only be <6>
R5C1 can only be <4>
R8C3 can only be <1>
R1C1 can only be <7>
R2C9 can only be <8>
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