May 25 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 can only be <6>
R2C8 can only be <7>
R3C3 can only be <2>
R2C2 can only be <8>
R1C4 is the only square in row 1 that can be <5>
R1C6 is the only square in row 1 that can be <7>
R8C4 is the only square in row 8 that can be <7>
R8C6 is the only square in row 8 that can be <1>
R5C6 can only be <9>
R5C4 can only be <1>
R9C9 is the only square in row 9 that can be <5>
Squares R5C1 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <4> from <234> leaving <23>
R5C9 - removing <4> from <234> leaving <23>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <6> from <269> leaving <29>
R9C5 - removing <8> from <2489> leaving <249>
Squares R6C2<27>, R6C3<69>, R6C5<68>, R6C7<79> and R6C9<28> in row 6 form a comprehensive naked set. These 5 squares can only contain the 5 possibilities <26789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <9> from <159> leaving <15>
R6C8 - removing <9> from <159> leaving <15>
Squares R3C4 and R3C7 in row 3 and R7C4 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 4 and 7 can be removed.
R4C7 - removing <4> from <3479> leaving <379>
R9C4 - removing <4> from <489> leaving <89>
Squares R1C5 and R1C9 in row 1, R5C2 and R5C9 in row 5 and R8C2 and R8C5 in row 8 form a Swordfish pattern on possibility <3>. All other instances of this possibility in columns 2, 5 and 9 can be removed.
R4C2 - removing <3> from <347> leaving <47>
R4C9 - removing <3> from <348> leaving <48>
Squares R7C3 (XY), R8C2 (XZ) and R7C7 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R8C8 - removing <4> from <49> leaving <9>
R7C7 can only be <4>
R3C7 can only be <3>
R3C6 can only be <8>
R1C9 can only be <4>
R1C5 can only be <3>
R4C9 can only be <8>
R3C4 can only be <4>
R9C6 can only be <2>
R4C5 can only be <6>
R6C9 can only be <2>
R6C2 can only be <7>
R5C9 can only be <3>
R2C6 can only be <6>
R8C5 can only be <4>
R2C4 can only be <9>
R7C6 can only be <3>
R6C5 can only be <8>
R5C2 can only be <2>
R6C7 can only be <9>
R4C2 can only be <4>
R6C3 can only be <6>
R4C7 can only be <7>
R7C3 can only be <9>
R8C2 can only be <3>
R9C5 can only be <9>
R9C1 can only be <4>
R9C4 can only be <8>
R2C5 can only be <2>
R7C4 can only be <6>
R4C8 can only be <1>
R5C1 can only be <5>
R4C1 can only be <9>
R6C8 can only be <5>
R5C8 can only be <4>
R6C1 can only be <1>
R4C3 can only be <3>
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