Dec 30 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <4>
R6C3 can only be <3>
R6C5 can only be <6>
R6C7 can only be <5>
R4C7 can only be <2>
R4C3 can only be <8>
R5C5 can only be <1>
R2C5 can only be <2>
R8C5 can only be <7>
R1C3 is the only square in row 1 that can be <4>
R2C4 is the only square in row 2 that can be <4>
R2C7 is the only square in row 2 that can be <8>
R8C8 is the only square in row 8 that can be <5>
R8C2 is the only square in row 8 that can be <6>
R8C6 is the only square in row 8 that can be <8>
R3C4 is the only square in column 4 that can be <5>
R7C6 is the only square in column 6 that can be <2>
R7C9 is the only square in column 9 that can be <7>
R7C1 can only be <3>
R7C4 can only be <1>
R8C4 can only be <3>
Squares R3C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <9> from <579> leaving <57>
R5C1 - removing <2> from <257> leaving <57>
Intersection of row 1 with block 3. The value <9> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <9> from <369> leaving <36>
Intersection of column 7 with block 9. The value <1> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C9 - removing <1> from <124> leaving <24>
Squares R3C1 and R8C1 in column 1 and R3C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 3 and 8 can be removed.
R8C3 - removing <2> from <129> leaving <19>
Squares R2C1, R5C1, R2C2 and R5C2 form a Type-3 Unique Rectangle on <57>. Upon close inspection, it is clear that:
(R2C2 or R5C2)<23> and R1C2<23> form a naked pair on <23> in column 2. No other squares in the column can contain these possibilities
R9C2 - removing <2> from <27> leaving <7>
Squares R2C8 (XY), R1C7 (XZ) and R5C8 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R5C7 - removing <9> from <49> leaving <4>
R1C8 - removing <9> from <239> leaving <23>
R5C9 can only be <6>
R8C7 can only be <1>
R5C8 can only be <9>
R2C9 can only be <1>
R8C3 can only be <9>
R9C7 can only be <3>
R9C8 can only be <2>
R1C7 can only be <9>
R9C3 can only be <1>
R1C8 can only be <3>
R8C9 can only be <4>
R1C2 can only be <2>
R2C8 can only be <6>
R2C6 can only be <9>
R3C9 can only be <2>
R3C1 can only be <9>
R8C1 can only be <2>
R2C3 can only be <7>
R5C2 can only be <5>
R2C1 can only be <5>
R5C3 can only be <2>
R3C6 can only be <1>
R5C1 can only be <7>
R2C2 can only be <3>
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