Aug 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <6>
R2C6 can only be <2>
R8C4 can only be <8>
R3C5 can only be <8>
R1C5 can only be <7>
R4C5 can only be <2>
R7C5 can only be <9>
R4C2 can only be <8>
R4C8 can only be <1>
R6C5 can only be <6>
R5C5 can only be <5>
R5C6 can only be <8>
R7C9 can only be <4>
R9C5 can only be <3>
R7C1 can only be <8>
R8C6 can only be <6>
R5C4 can only be <4>
R2C9 is the only square in row 2 that can be <3>
R2C1 is the only square in row 2 that can be <7>
R8C9 is the only square in row 8 that can be <7>
R5C7 is the only square in row 5 that can be <7>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <5> from <2456> leaving <246>
R1C8 - removing <5> from <2458> leaving <248>
R9C2 - removing <5> from <24569> leaving <2469>
R9C8 - removing <5> from <2589> leaving <289>
Squares R3C1, R3C9, R1C1 and R1C9 form a Type-4 Unique Rectangle on <12>.
R1C1 - removing <2> from <1246> leaving <146>
R1C9 - removing <2> from <125> leaving <15>
Squares R1C7, R9C7, R1C8 and R9C8 form a Type-4 Unique Rectangle on <28>.
R1C8 - removing <2> from <248> leaving <48>
R9C8 - removing <2> from <289> leaving <89>
Squares R9C8 (XY), R9C7 (XZ) and R6C8 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R8C8 - removing <2> from <259> leaving <59>
R6C8 is the only square in column 8 that can be <2>
R6C2 can only be <9>
R5C9 can only be <9>
Intersection of row 8 with block 7. The value <2> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <2> from <2469> leaving <469>
R9C2 - removing <2> from <246> leaving <46>
R9C3 - removing <2> from <256> leaving <56>
Squares R9C2 (XY), R2C2 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R1C3 - removing <5> from <256> leaving <26>
R8C2 - removing <5> from <25> leaving <2>
R8C1 can only be <9>
R8C8 can only be <5>
R2C8 can only be <4>
R9C9 can only be <2>
R9C7 can only be <8>
R3C9 can only be <1>
R2C2 can only be <5>
R1C8 can only be <8>
R3C1 can only be <2>
R1C9 can only be <5>
R9C8 can only be <9>
R1C7 can only be <2>
R1C3 can only be <6>
R5C1 can only be <6>
R5C3 can only be <2>
R9C1 can only be <4>
R9C2 can only be <6>
R1C1 can only be <1>
R9C3 can only be <5>
R1C2 can only be <4>
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