Jan 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 can only be <4>
R6C1 can only be <3>
R6C9 can only be <1>
R5C1 can only be <5>
R6C5 can only be <8>
R4C9 can only be <9>
R4C5 can only be <1>
R5C9 can only be <3>
R5C3 can only be <1>
R2C1 can only be <7>
R8C1 can only be <2>
R5C7 can only be <2>
R9C1 can only be <9>
R1C1 can only be <8>
R1C2 is the only square in row 1 that can be <1>
R3C8 is the only square in row 3 that can be <8>
R7C8 is the only square in row 7 that can be <9>
R8C9 is the only square in row 8 that can be <8>
R9C4 is the only square in row 9 that can be <1>
R9C5 is the only square in row 9 that can be <2>
R3C4 is the only square in row 3 that can be <2>
R9C6 is the only square in row 9 that can be <8>
Squares R3C6 and R5C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <4> from <346> leaving <36>
R7C6 - removing <4> from <346> leaving <36>
Intersection of block 9 with row 9. The value <5> only appears in one or more of squares R9C7, R9C8 and R9C9 of block 9. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C2 - removing <5> from <345> leaving <34>
Squares R2C5 and R2C7 in row 2 and R8C5 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 5 and 7 can be removed.
R1C5 - removing <3> from <34567> leaving <4567>
R7C5 - removing <3> from <3456> leaving <456>
Squares R2C3 and R8C3 in column 3 and R2C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C5 - removing <4> from <3456> leaving <356>
R8C5 - removing <4> from <345> leaving <35>
R2C9 - removing <4> from <456> leaving <56>
Intersection of block 8 with row 7. The values <46> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C2 - removing <4> from <345> leaving <35>
Squares R3C6, R5C6, R3C5 and R5C5 form a Type-4 Unique Rectangle on <49>.
R3C5 - removing <4> from <459> leaving <59>
R5C5 - removing <4> from <479> leaving <79>
Squares R1C8 (XY), R1C6 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R2C5 - removing <6> from <356> leaving <35>
R1C9 - removing <6> from <456> leaving <45>
R2C9 is the only square in row 2 that can be <6>
Squares R2C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <5> from <4567> leaving <467>
R3C5 - removing <5> from <59> leaving <9>
R7C5 - removing <5> from <456> leaving <46>
R3C6 can only be <4>
R5C5 can only be <7>
R3C2 can only be <5>
R5C6 can only be <9>
R5C4 can only be <4>
R1C5 can only be <6>
R1C6 can only be <3>
R7C5 can only be <4>
R1C8 can only be <5>
R7C6 can only be <6>
R2C5 can only be <5>
R1C4 can only be <7>
R1C9 can only be <4>
R9C8 can only be <3>
R9C9 can only be <5>
R2C7 can only be <3>
R2C3 can only be <4>
R8C5 can only be <3>
R8C7 can only be <4>
R7C2 can only be <3>
R7C4 can only be <5>
R9C2 can only be <4>
R8C3 can only be <5>
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