Nov 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <5>
R6C4 can only be <8>
R6C6 can only be <2>
R4C6 can only be <1>
R3C4 can only be <9>
R7C4 can only be <6>
R5C5 can only be <6>
R3C3 is the only square in row 3 that can be <8>
Squares R1C1 and R1C9 in row 1 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.
R1C3 - removing <47> from <3467> leaving <36>
R1C5 - removing <4> from <134> leaving <13>
R1C7 - removing <47> from <13467> leaving <136>
Intersection of block 4 with column 3. The value <4> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R2C3 - removing <4> from <2345> leaving <235>
R7C3 - removing <4> from <134579> leaving <13579>
R8C3 - removing <4> from <4569> leaving <569>
R9C3 - removing <4> from <4567> leaving <567>
Intersection of block 6 with column 7. The value <4> only appears in one or more of squares R4C7, R5C7 and R6C7 of block 6. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain this value.
R2C7 - removing <4> from <2349> leaving <239>
R3C7 - removing <4> from <123467> leaving <12367>
R7C7 - removing <4> from <245789> leaving <25789>
R8C7 - removing <4> from <24569> leaving <2569>
R9C7 - removing <4> from <45678> leaving <5678>
Squares R1C1<47>, R1C3<36>, R2C2<34> and R3C2<3467> in block 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3467>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <3> from <235> leaving <25>
R3C1 - removing <47> from <2457> leaving <25>
Squares R7C1<4579>, R8C2<46>, R8C3<569>, R9C1<457> and R9C3<567> in block 7 form a comprehensive naked set. These 5 squares can only contain the 5 possibilities <45679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <47> from <1347> leaving <13>
R7C3 - removing <579> from <13579> leaving <13>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C7 - removing <6> from <12367> leaving <1237>
R8C3 - removing <6> from <569> leaving <59>
R8C7 - removing <6> from <2569> leaving <259>
Squares R5C1 and R7C1 in column 1 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 5 and 7 can be removed.
R5C3 - removing <9> from <1279> leaving <127>
R5C7 - removing <9> from <5789> leaving <578>
R7C7 - removing <9> from <25789> leaving <2578>
R5C8 - removing <9> from <789> leaving <78>
R7C8 - removing <9> from <4789> leaving <478>
Squares R2C2 (XY), R1C3 (XZ) and R8C2 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R3C2 - removing <6> from <3467> leaving <347>
R9C3 - removing <6> from <567> leaving <57>
R3C8 is the only square in row 3 that can be <6>
R1C3 is the only square in row 1 that can be <6>
R8C2 is the only square in row 8 that can be <6>
R9C7 is the only square in row 9 that can be <6>
R9C5 is the only square in row 9 that can be <8>
R7C3 is the only square in column 3 that can be <3>
R7C2 can only be <1>
R5C2 can only be <7>
R5C8 can only be <8>
R6C3 can only be <4>
R5C7 can only be <5>
R6C7 can only be <7>
R4C3 can only be <9>
R4C7 can only be <4>
R8C3 can only be <5>
R5C1 can only be <2>
R5C3 can only be <1>
R3C1 can only be <5>
R5C9 can only be <9>
R2C3 can only be <2>
R9C3 can only be <7>
R9C1 can only be <4>
R3C6 can only be <4>
R3C2 can only be <3>
R7C6 can only be <5>
R9C9 can only be <5>
R1C1 can only be <7>
R7C1 can only be <9>
R1C9 can only be <4>
R2C8 can only be <9>
R2C7 can only be <3>
R8C8 can only be <4>
R3C5 can only be <1>
R2C2 can only be <4>
R3C7 can only be <2>
R1C5 can only be <3>
R3C9 can only be <7>
R7C7 can only be <8>
R8C7 can only be <9>
R7C9 can only be <2>
R7C5 can only be <4>
R8C5 can only be <2>
R7C8 can only be <7>
R1C7 can only be <1>
R2C5 can only be <5>
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