Nov 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <6>
R1C6 can only be <2>
R3C3 can only be <5>
R3C5 can only be <3>
R5C1 is the only square in row 5 that can be <5>
R5C5 is the only square in row 5 that can be <6>
R5C3 is the only square in row 5 that can be <8>
R5C6 is the only square in row 5 that can be <9>
R9C6 can only be <1>
R9C9 is the only square in row 9 that can be <8>
R9C7 is the only square in row 9 that can be <5>
R9C1 is the only square in row 9 that can be <6>
R8C9 is the only square in row 8 that can be <6>
R3C7 is the only square in row 3 that can be <6>
R6C1 is the only square in block 4 that can be <3>
Squares R9C2 and R9C4 in row 9 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.
R9C3 - removing <4> from <34> leaving <3>
R9C5 - removing <47> from <2479> leaving <29>
R7C3 can only be <1>
R1C3 can only be <4>
Intersection of block 3 with column 9. The values <25> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain these values.
R5C9 - removing <2> from <12347> leaving <1347>
R7C9 - removing <2> from <239> leaving <39>
Squares R5C2 and R9C2 in column 2 and R5C4 and R9C4 in column 4 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C9 - removing <4> from <1347> leaving <137>
Squares R3C1 and R3C9 in row 3, R4C5 and R4C9 in row 4 and R7C1 and R7C5 in row 7 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 1, 5 and 9 can be removed.
R1C1 - removing <7> from <178> leaving <18>
R1C9 - removing <7> from <3579> leaving <359>
R5C9 - removing <7> from <137> leaving <13>
Squares R9C8 (XY), R5C8 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R5C9 - removing <3> from <13> leaving <1>
R5C2 can only be <4>
R6C9 can only be <4>
R6C5 can only be <1>
R4C9 can only be <7>
R3C9 can only be <2>
R5C4 can only be <7>
R9C2 can only be <7>
R4C1 can only be <1>
R9C4 can only be <4>
R4C5 can only be <4>
R1C2 can only be <1>
R7C1 can only be <9>
R8C5 can only be <9>
R1C1 can only be <8>
R3C1 can only be <7>
R2C9 can only be <5>
R7C9 can only be <3>
R8C1 can only be <4>
R7C7 can only be <2>
R9C5 can only be <2>
R9C8 can only be <9>
R7C5 can only be <7>
R1C8 can only be <3>
R1C5 can only be <5>
R2C1 can only be <2>
R1C9 can only be <9>
R2C5 can only be <8>
R1C7 can only be <7>
R5C8 can only be <2>
R5C7 can only be <3>
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