Aug 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C7 can only be <7>
R8C9 can only be <1>
R5C7 can only be <9>
R9C8 can only be <6>
R9C2 can only be <9>
R9C5 can only be <7>
R2C7 can only be <8>
R1C8 is the only square in row 1 that can be <1>
R2C8 is the only square in row 2 that can be <9>
R4C5 is the only square in row 4 that can be <8>
R4C4 is the only square in row 4 that can be <9>
R6C4 is the only square in row 6 that can be <1>
R8C2 is the only square in row 8 that can be <8>
R8C1 is the only square in row 8 that can be <5>
R4C2 is the only square in column 2 that can be <3>
Squares R2C3 and R5C3 in column 3 and R2C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C2 - removing <2> from <24567> leaving <4567>
R2C4 - removing <2> from <235> leaving <35>
R5C4 - removing <2> from <235> leaving <35>
R5C5 - removing <2> from <23456> leaving <3456>
R2C6 - removing <2> from <234> leaving <34>
R5C6 - removing <2> from <23467> leaving <3467>
R8C4 is the only square in column 4 that can be <2>
Intersection of column 6 with block 5. The values <27> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R6C5 - removing <2> from <256> leaving <56>
Squares R2C4 and R5C4 in column 4 and R2C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C2 - removing <5> from <4567> leaving <467>
R5C5 - removing <5> from <3456> leaving <346>
Squares R4C6, R4C8, R6C6 and R6C8 form a Type-3 Unique Rectangle on <27>. Upon close inspection, it is clear that:
(R6C6 or R6C8)<56> and R6C5<56> form a naked pair on <56> in row 6. No other squares in the row can contain these possibilities
R6C2 - removing <6> from <267> leaving <27>
Intersection of row 6 with block 5. The value <6> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <6> from <346> leaving <34>
R5C6 - removing <6> from <3467> leaving <347>
Squares R6C5 (XY), R5C4 (XZ) and R7C5 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R5C5 - removing <3> from <34> leaving <4>
R3C2 is the only square in row 3 that can be <4>
R7C2 can only be <6>
R7C5 can only be <3>
R2C2 can only be <7>
R8C3 can only be <4>
R7C8 can only be <4>
R8C6 can only be <6>
R8C8 can only be <3>
R2C1 can only be <6>
R6C2 can only be <2>
R6C6 can only be <7>
R1C2 can only be <5>
R5C3 can only be <6>
R6C8 can only be <5>
R4C6 can only be <2>
R5C6 can only be <3>
R6C5 can only be <6>
R3C8 can only be <2>
R5C9 can only be <2>
R1C5 can only be <2>
R3C5 can only be <5>
R2C3 can only be <2>
R5C1 can only be <7>
R2C9 can only be <5>
R2C4 can only be <3>
R4C8 can only be <7>
R5C4 can only be <5>
R2C6 can only be <4>
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