Dec 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C6 can only be <9>
R7C5 can only be <4>
R8C5 can only be <3>
R8C8 can only be <9>
R7C4 can only be <6>
R5C5 can only be <2>
R5C6 can only be <3>
R2C5 can only be <9>
R3C5 can only be <8>
R5C4 can only be <4>
R2C9 is the only square in row 2 that can be <7>
R6C2 is the only square in column 2 that can be <8>
R3C6 is the only square in column 6 that can be <5>
R6C8 is the only square in column 8 that can be <1>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <7> from <6789> leaving <689>
Intersection of column 3 with block 4. The value <5> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C1 - removing <5> from <1579> leaving <179>
R6C1 - removing <5> from <2345> leaving <234>
Intersection of column 7 with block 6. The values <57> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R5C9 - removing <5> from <59> leaving <9>
R6C9 - removing <5> from <2345> leaving <234>
R1C7 is the only square in row 1 that can be <9>
Squares R2C2 and R4C2 in column 2 and R2C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 2 and 4 can be removed.
R2C1 - removing <3> from <235> leaving <25>
R4C1 - removing <3> from <23479> leaving <2479>
R4C7 - removing <3> from <367> leaving <67>
R4C9 - removing <3> from <2346> leaving <246>
Squares R9C4, R9C6, R1C4 and R1C6 form a Type-1 Unique Rectangle on <27>.
R1C4 - removing <27> from <237> leaving <3>
R3C4 can only be <2>
R9C4 can only be <7>
R1C6 can only be <7>
R9C6 can only be <2>
Squares R5C1 (XY), R3C1 (XZ) and R4C2 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R2C2 - removing <3> from <35> leaving <5>
R6C1 - removing <3> from <234> leaving <24>
R2C1 can only be <2>
R8C2 can only be <7>
R4C2 can only be <3>
R2C8 can only be <3>
R6C1 can only be <4>
R4C8 can only be <2>
R3C9 can only be <1>
R3C1 can only be <3>
R1C9 can only be <2>
R4C3 can only be <9>
R6C9 can only be <3>
R6C7 can only be <5>
R4C1 can only be <7>
R9C3 can only be <8>
R6C3 can only be <2>
R5C7 can only be <7>
R9C9 can only be <6>
R1C3 can only be <1>
R7C1 can only be <5>
R9C1 can only be <9>
R9C7 can only be <3>
R4C9 can only be <4>
R8C9 can only be <5>
R1C1 can only be <8>
R5C3 can only be <5>
R4C7 can only be <6>
R5C1 can only be <1>
R7C9 can only be <8>
R8C1 can only be <6>
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