Jan 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <8>
R2C5 can only be <1>
R8C1 can only be <8>
R2C9 can only be <6>
R3C6 can only be <4>
R2C1 can only be <4>
R1C7 can only be <1>
R3C7 can only be <7>
R7C1 can only be <1>
R3C9 can only be <9>
R3C1 can only be <5>
R3C3 can only be <1>
R3C4 can only be <8>
R1C2 can only be <9>
R1C3 can only be <6>
R5C1 is the only square in row 5 that can be <6>
R6C9 is the only square in row 6 that can be <1>
R7C6 is the only square in row 7 that can be <9>
R9C6 is the only square in row 9 that can be <1>
R6C6 is the only square in column 6 that can be <6>
R7C9 is the only square in column 9 that can be <2>
Squares R4C1 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C4 - removing <23> from <2357> leaving <57>
R4C7 - removing <3> from <348> leaving <48>
R4C9 - removing <3> from <357> leaving <57>
Squares R4C4 and R4C9 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C3 - removing <5> from <458> leaving <48>
Squares R9C2<45>, R9C3<457> and R9C8<47> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <457>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <7> from <2367> leaving <236>
R9C5 - removing <7> from <237> leaving <23>
R9C7 - removing <4> from <346> leaving <36>
Squares R5C5 and R5C9 in row 5 and R8C5 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 5 and 9 can be removed.
R1C5 - removing <3> from <235> leaving <25>
R9C5 - removing <3> from <23> leaving <2>
R1C5 can only be <5>
Squares R4C3 and R4C7 in row 4 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 7 can be removed.
R9C3 - removing <4> from <457> leaving <57>
Squares R5C8 (XY), R5C2 (XZ) and R4C9 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R5C9 - removing <5> from <357> leaving <37>
R5C2 is the only square in row 5 that can be <5>
R9C2 can only be <4>
R6C3 can only be <8>
R6C7 can only be <3>
R4C3 can only be <4>
R6C1 can only be <2>
R9C7 can only be <6>
R5C9 can only be <7>
R9C8 can only be <7>
R7C3 can only be <7>
R9C4 can only be <3>
R7C7 can only be <4>
R9C3 can only be <5>
R5C8 can only be <4>
R8C9 can only be <3>
R4C7 can only be <8>
R5C5 can only be <3>
R4C9 can only be <5>
R6C4 can only be <5>
R4C1 can only be <3>
R4C4 can only be <7>
R7C4 can only be <6>
R8C5 can only be <7>
R1C4 can only be <2>
R1C6 can only be <3>
R4C6 can only be <2>
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