Oct 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <2>
R2C6 can only be <7>
R5C5 can only be <8>
R8C6 can only be <1>
R3C6 can only be <9>
R3C5 can only be <5>
R7C6 can only be <4>
R3C4 can only be <8>
R7C5 can only be <2>
R1C7 is the only square in row 1 that can be <8>
R4C7 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <5>
R3C7 is the only square in column 7 that can be <7>
Squares R6C2 and R7C2 in column 2 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 column.
R3C2 - removing <6> from <246> leaving <24>
R4C2 - removing <8> from <248> leaving <24>
Squares R5C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <2> from <127> leaving <17>
R3C3 - removing <26> from <12346> leaving <134>
R4C3 - removing <2> from <248> leaving <48>
R7C3 - removing <6> from <6789> leaving <789>
R9C3 - removing <2> from <29> leaving <9>
R3C1 is the only square in row 3 that can be <6>
R7C9 is the only square in row 7 that can be <9>
Intersection of column 9 with block 3. The value <1> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <1> from <123> leaving <23>
Squares R8C7<25>, R9C7<245> and R9C9<24> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <245>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C7 - removing <5> from <135> leaving <13>
Squares R5C3 and R5C7 in row 5 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 7 can be removed.
R9C7 - removing <2> from <245> leaving <45>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C9 - removing <2> from <124> leaving <14>
Squares R3C2 (XY), R3C8 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R2C7 - removing <3> from <34> leaving <4>
R3C3 - removing <3> from <134> leaving <14>
R2C3 can only be <3>
R9C7 can only be <5>
R3C9 can only be <1>
R3C3 can only be <4>
R1C9 can only be <2>
R9C1 can only be <2>
R8C7 can only be <2>
R1C1 can only be <7>
R9C9 can only be <4>
R3C8 can only be <3>
R3C2 can only be <2>
R4C3 can only be <8>
R7C8 can only be <1>
R4C8 can only be <2>
R7C3 can only be <7>
R6C2 can only be <6>
R4C2 can only be <4>
R5C7 can only be <6>
R5C3 can only be <2>
R6C7 can only be <1>
R7C2 can only be <8>
R6C8 can only be <8>
R7C7 can only be <3>
R7C1 can only be <5>
R1C3 can only be <1>
R8C3 can only be <6>
R7C4 can only be <6>
R8C4 can only be <5>
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