Oct 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 can only be <7>
R6C5 can only be <3>
R3C6 can only be <2>
R2C5 can only be <5>
R4C6 can only be <6>
R6C6 can only be <9>
R4C5 can only be <2>
R6C4 can only be <8>
R8C5 can only be <7>
R6C1 can only be <6>
R4C4 can only be <1>
R7C6 can only be <5>
R5C4 can only be <5>
R5C6 can only be <7>
R7C4 can only be <9>
R6C9 can only be <4>
R1C1 is the only square in row 1 that can be <2>
R1C9 is the only square in row 1 that can be <9>
R1C8 is the only square in row 1 that can be <5>
R5C9 is the only square in row 5 that can be <2>
Squares R9C2 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <38> from <35789> leaving <579>
R9C3 - removing <38> from <3789> leaving <79>
R9C7 - removing <3> from <137> leaving <17>
R9C9 - removing <38> from <13578> leaving <157>
Squares R1C3 and R5C3 in column 3 and R1C7 and R5C7 in column 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 1 and 5 can be removed.
R5C1 - removing <3> from <1389> leaving <189>
R1C2 - removing <3> from <34> leaving <4>
R5C2 - removing <3> from <138> leaving <18>
R5C8 - removing <3> from <368> leaving <68>
R3C8 is the only square in row 3 that can be <4>
R7C1 is the only square in row 7 that can be <4>
R7C9 is the only square in row 7 that can be <7>
R9C7 can only be <1>
R9C9 can only be <5>
R8C7 is the only square in row 8 that can be <4>
R8C1 is the only square in row 8 that can be <5>
Intersection of block 7 with column 2. The value <3> only appears in one or more of squares R7C2, R8C2 and R9C2 of block 7. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain this value.
R3C2 - removing <3> from <136> leaving <16>
Squares R5C2 and R9C2 in column 2 and R5C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C1 - removing <8> from <189> leaving <19>
R5C3 - removing <8> from <389> leaving <39>
Squares R1C3<37>, R5C3<39> and R9C3<79> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <7> from <678> leaving <68>
Squares R4C1 (XY), R3C1 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R5C1 - removing <1> from <19> leaving <9>
R3C2 - removing <1> from <16> leaving <6>
R7C2 can only be <3>
R2C3 can only be <8>
R5C3 can only be <3>
R9C1 can only be <7>
R5C7 can only be <6>
R1C3 can only be <7>
R4C1 can only be <8>
R5C8 can only be <8>
R2C7 can only be <7>
R5C2 can only be <1>
R9C8 can only be <3>
R4C9 can only be <3>
R7C8 can only be <6>
R9C2 can only be <8>
R8C9 can only be <8>
R8C3 can only be <6>
R9C3 can only be <9>
R1C7 can only be <3>
R3C9 can only be <1>
R2C1 can only be <1>
R3C1 can only be <3>
R2C9 can only be <6>
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