Oct 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <7>
R8C4 can only be <8>
R8C5 can only be <3>
R4C8 can only be <3>
R6C4 can only be <1>
R4C6 can only be <2>
R5C8 can only be <8>
R6C8 can only be <7>
R5C9 can only be <2>
R5C2 can only be <1>
R6C2 can only be <2>
R2C4 can only be <9>
R8C6 can only be <6>
R5C5 can only be <9>
R9C5 can only be <1>
R4C2 can only be <6>
R2C6 can only be <8>
R6C6 can only be <3>
R5C1 can only be <3>
Squares R1C2<589>, R2C2<45>, R3C1<48> and R3C3<59> in block 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <4589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <8> from <1268> leaving <126>
R1C3 - removing <59> from <2569> leaving <26>
R2C1 - removing <4> from <1246> leaving <126>
Squares R1C3 and R9C3 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.
R7C3 - removing <6> from <569> leaving <59>
Squares R7C1<68>, R8C1<47>, R9C1<24678>, R9C2<48> and R9C3<26> in block 7 form a comprehensive naked set. These 5 squares can only contain the 5 possibilities <24678>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C2 - removing <4> from <459> leaving <59>
Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C7 - removing <5> from <3568> leaving <368>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 9 can be removed.
R1C9 - removing <9> from <1389> leaving <138>
R8C9 - removing <9> from <479> leaving <47>
Squares R8C1 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <4> from <459> leaving <59>
Squares R3C1 and R3C9 in row 3 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.
R2C9 - removing <4> from <14> leaving <1>
R9C1 - removing <4> from <24678> leaving <2678>
R9C9 - removing <4> from <3478> leaving <378>
R1C1 is the only square in row 1 that can be <1>
Squares R3C1 (XY), R2C2 (XZ) and R3C7 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R3C3 - removing <5> from <59> leaving <9>
R2C8 - removing <5> from <456> leaving <46>
R7C3 can only be <5>
R8C2 can only be <9>
R8C8 can only be <5>
R1C8 is the only square in row 1 that can be <9>
R3C7 is the only square in row 3 that can be <5>
R7C9 is the only square in row 7 that can be <9>
Squares R9C2 (XY), R9C8 (XZ) and R7C1 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R7C7 - removing <6> from <68> leaving <8>
R9C1 - removing <6> from <2678> leaving <278>
R9C3 - removing <6> from <26> leaving <2>
R7C1 can only be <6>
R1C3 can only be <6>
R1C7 can only be <3>
R2C1 can only be <2>
R1C9 can only be <8>
R9C7 can only be <6>
R1C2 can only be <5>
R3C9 can only be <4>
R2C5 can only be <5>
R2C2 can only be <4>
R1C5 can only be <2>
R3C1 can only be <8>
R8C9 can only be <7>
R2C8 can only be <6>
R8C1 can only be <4>
R9C9 can only be <3>
R9C8 can only be <4>
R9C2 can only be <8>
R9C1 can only be <7>
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