Oct 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <8>
R2C8 is the only square in row 2 that can be <6>
R8C8 can only be <8>
R8C9 can only be <6>
R8C4 can only be <7>
R8C2 can only be <4>
R3C9 is the only square in row 3 that can be <7>
R4C1 is the only square in row 4 that can be <5>
R6C9 is the only square in row 6 that can be <8>
R9C3 is the only square in row 9 that can be <8>
R2C1 is the only square in column 1 that can be <4>
R2C6 can only be <2>
R2C2 can only be <1>
R9C1 is the only square in row 9 that can be <1>
R5C3 is the only square in column 3 that can be <1>
R6C6 is the only square in column 6 that can be <3>
R4C7 is the only square in column 7 that can be <6>
R4C8 is the only square in row 4 that can be <1>
R9C8 is the only square in column 8 that can be <5>
Intersection of column 8 with block 3. The value <3> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <3> from <1234> leaving <124>
R1C9 - removing <3> from <2349> leaving <249>
R3C7 - removing <3> from <1234> leaving <124>
Squares R4C2 and R4C9 in row 4 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 9 can be removed.
R1C2 - removing <3> from <23> leaving <2>
R5C9 - removing <3> from <2349> leaving <249>
R7C2 - removing <3> from <3679> leaving <679>
R3C3 can only be <3>
R7C3 can only be <6>
R6C3 can only be <2>
R6C8 can only be <9>
R6C1 can only be <7>
R1C8 can only be <3>
R3C8 can only be <2>
R6C2 can only be <6>
R7C2 is the only square in row 7 that can be <7>
R1C9 is the only square in column 9 that can be <9>
R5C9 is the only square in column 9 that can be <4>
Intersection of column 6 with block 8. The value <9> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <9> from <259> leaving <25>
R9C4 - removing <9> from <269> leaving <26>
R9C5 - removing <9> from <2469> leaving <246>
Squares R5C5 and R5C7 in row 5 and R7C5 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 7 can be removed.
R9C5 - removing <2> from <246> leaving <46>
Squares R1C5 (XYZ), R1C6 (XZ) and R9C5 (YZ) form an XYZ-Wing pattern on <4>. All squares that are buddies of all three squares cannot be <4>.
R3C5 - removing <4> from <49> leaving <9>
R3C4 can only be <1>
R5C5 can only be <2>
R5C7 can only be <3>
R7C5 can only be <5>
R4C4 can only be <9>
R5C1 can only be <9>
R7C7 can only be <2>
R4C9 can only be <2>
R7C6 can only be <9>
R7C1 can only be <3>
R9C6 can only be <4>
R9C9 can only be <3>
R9C5 can only be <6>
R1C6 can only be <5>
R9C2 can only be <9>
R3C7 can only be <4>
R1C4 can only be <6>
R1C7 can only be <1>
R4C2 can only be <3>
R9C4 can only be <2>
R1C5 can only be <4>
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