May 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <8>
R5C8 is the only square in row 5 that can be <5>
R5C4 is the only square in row 5 that can be <7>
R6C1 is the only square in row 6 that can be <7>
R7C7 is the only square in column 7 that can be <1>
R7C4 can only be <2>
R7C3 is the only square in row 7 that can be <4>
R9C9 is the only square in row 9 that can be <4>
R6C9 can only be <9>
R9C1 is the only square in row 9 that can be <2>
R8C9 is the only square in row 8 that can be <2>
R2C8 is the only square in column 8 that can be <1>
R8C1 is the only square in block 7 that can be <1>
Squares R8C2 and R9C2 in column 2 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 column.
R1C2 - removing <3> from <346> leaving <46>
R2C2 - removing <3> from <369> leaving <69>
R5C2 - removing <38> from <3489> leaving <49>
Squares R7C5 and R7C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <3> from <389> leaving <89>
R9C6 - removing <3> from <138> leaving <18>
Intersection of row 3 with block 2. The values <25> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C6 - removing <5> from <135> leaving <13>
R2C5 - removing <5> from <359> leaving <39>
Squares R3C3<39>, R3C4<69> and R3C7<36> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C5 - removing <39> from <2359> leaving <25>
R3C6 - removing <3> from <235> leaving <25>
Squares R3C3 and R3C7 in row 3 and R5C3 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
R4C3 - removing <3> from <138> leaving <18>
R4C7 - removing <3> from <3468> leaving <468>
Squares R4C3 and R6C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C3 - removing <8> from <389> leaving <39>
Squares R4C3, R6C3, R4C5 and R6C5 form a Type-2 Unique Rectangle on <18>.
R5C5 - removing <4> from <248> leaving <28>
Squares R5C5 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C7 - removing <8> from <348> leaving <34>
Squares R5C5 and R5C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <8> from <148> leaving <14>
R6C5 - removing <8> from <148> leaving <14>
Squares R3C3 (XY), R3C7 (XZ) and R2C2 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R2C9 - removing <6> from <356> leaving <35>
R2C2 is the only square in row 2 that can be <6>
R1C2 can only be <4>
R5C2 can only be <9>
R5C3 can only be <3>
R5C7 can only be <4>
R3C3 can only be <9>
R4C1 can only be <4>
R6C7 can only be <8>
R6C3 can only be <1>
R4C7 can only be <6>
R3C4 can only be <6>
R3C7 can only be <3>
R1C4 can only be <1>
R2C9 can only be <5>
R4C5 can only be <1>
R4C3 can only be <8>
R6C5 can only be <4>
R4C9 can only be <3>
R1C6 can only be <3>
R9C4 can only be <9>
R1C1 can only be <5>
R7C6 can only be <5>
R2C5 can only be <9>
R8C5 can only be <8>
R2C1 can only be <3>
R1C9 can only be <6>
R7C5 can only be <3>
R3C6 can only be <2>
R8C2 can only be <3>
R5C5 can only be <2>
R9C6 can only be <1>
R9C8 can only be <3>
R9C2 can only be <8>
R8C8 can only be <9>
R3C5 can only be <5>
R5C6 can only be <8>
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