Jun 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 can only be <4>
R4C7 can only be <9>
R9C1 can only be <8>
R8C1 can only be <9>
R5C1 can only be <2>
R1C5 is the only square in row 1 that can be <9>
R3C7 is the only square in row 3 that can be <2>
R4C5 is the only square in row 4 that can be <2>
R7C3 is the only square in row 7 that can be <2>
R7C8 is the only square in row 7 that can be <9>
R8C4 is the only square in row 8 that can be <8>
R5C6 is the only square in row 5 that can be <8>
R5C2 is the only square in row 5 that can be <9>
R6C6 is the only square in row 6 that can be <9>
R1C3 is the only square in column 3 that can be <8>
R1C9 can only be <4>
R3C6 is the only square in column 6 that can be <5>
R1C4 can only be <7>
R1C8 can only be <5>
R4C6 is the only square in row 4 that can be <7>
R5C3 is the only square in row 5 that can be <7>
R3C3 can only be <1>
R8C3 can only be <5>
R6C3 can only be <3>
R6C2 can only be <5>
R5C4 is the only square in row 5 that can be <5>
R9C7 is the only square in row 9 that can be <5>
R9C5 is the only square in row 9 that can be <7>
Squares R3C4 and R4C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C4 - removing <36> from <1346> leaving <14>
Squares R6C4 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C5 - removing <14> from <1346> leaving <36>
Squares R5C5 and R5C9 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <36> from <1346> leaving <14>
Intersection of block 8 with column 6. The value <3> only appears in one or more of squares R7C6, R8C6 and R9C6 of block 8. These squares are the ones that intersect with column 6. Thus, the other (non-intersecting) squares of column 6 cannot contain this value.
R2C6 - removing <3> from <346> leaving <46>
Squares R3C4 and R3C8 in row 3 and R4C4 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 4 and 8 can be removed.
R2C8 - removing <3> from <137> leaving <17>
Squares R9C2, R9C6, R7C2 and R7C6 form a Type-4 Unique Rectangle on <34>.
R7C2 - removing <4> from <134> leaving <13>
R7C6 - removing <4> from <346> leaving <36>
Squares R7C2 (XY), R7C4 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R9C6 - removing <4> from <34> leaving <3>
R9C2 can only be <4>
R7C6 can only be <6>
R7C9 can only be <8>
R2C6 can only be <4>
R7C7 can only be <4>
R2C9 can only be <3>
R8C2 can only be <1>
R2C5 can only be <6>
R5C9 can only be <6>
R3C8 can only be <7>
R3C2 can only be <6>
R2C8 can only be <1>
R5C5 can only be <3>
R4C8 can only be <3>
R7C4 can only be <1>
R5C7 can only be <1>
R8C8 can only be <6>
R8C5 can only be <4>
R7C2 can only be <3>
R6C5 can only be <1>
R2C2 can only be <7>
R3C4 can only be <3>
R2C7 can only be <8>
R5C8 can only be <4>
R4C4 can only be <6>
R6C4 can only be <4>
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