Feb 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <7>
R2C5 can only be <8>
R5C2 can only be <1>
R2C7 can only be <5>
R1C3 is the only square in row 1 that can be <1>
R4C6 is the only square in row 4 that can be <5>
Squares R1C7 and R8C7 in column 7 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 column.
R5C7 - removing <7> from <378> leaving <38>
R9C7 - removing <47> from <3478> leaving <38>
Intersection of row 3 with block 1. The value <9> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <9> from <349> leaving <34>
Intersection of column 3 with block 7. The value <4> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <4> from <24789> leaving <2789>
R7C2 - removing <4> from <49> leaving <9>
R9C1 - removing <4> from <2478> leaving <278>
R3C2 can only be <4>
R3C8 can only be <8>
R1C1 can only be <3>
R3C9 can only be <6>
R5C8 can only be <7>
R3C5 can only be <3>
R1C9 can only be <7>
R7C8 can only be <4>
R8C7 can only be <7>
R1C7 can only be <4>
R3C1 can only be <9>
R5C5 is the only square in column 5 that can be <6>
Squares R4C1 and R4C9 in row 4 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R6C1 - removing <8> from <248> leaving <24>
R6C9 - removing <8> from <18> leaving <1>
R9C1 - removing <8> from <278> leaving <27>
R9C9 - removing <8> from <238> leaving <23>
R4C5 is the only square in row 4 that can be <1>
R6C6 is the only square in row 6 that can be <8>
Squares R6C1 (XY), R9C1 (XZ) and R6C4 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R9C4 - removing <7> from <467> leaving <46>
R9C1 is the only square in row 9 that can be <7>
R7C5 is the only square in row 7 that can be <7>
R6C4 is the only square in row 6 that can be <7>
Squares R6C1 and R8C3 form a remote naked pair. <24> can be removed from any square that is common to their groups.
R5C3 - removing <2> from <28> leaving <8>
R7C1 - removing <2> from <28> leaving <8>
R5C7 can only be <3>
R4C1 can only be <4>
R5C4 can only be <9>
R9C7 can only be <8>
R4C9 can only be <8>
R7C9 can only be <2>
R9C9 can only be <3>
R4C4 can only be <3>
R6C1 can only be <2>
R5C6 can only be <2>
R1C4 can only be <6>
R9C6 can only be <6>
R6C5 can only be <4>
R8C5 can only be <2>
R8C3 can only be <4>
R9C4 can only be <4>
R1C6 can only be <9>
R9C3 can only be <2>
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