Feb 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 can only be <6>
R8C1 can only be <7>
R5C5 is the only square in row 5 that can be <5>
Squares R5C1 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <2> from <237> leaving <37>
R5C6 - removing <1> from <134> leaving <34>
R5C8 - removing <1> from <16789> leaving <6789>
R2C6 is the only square in column 6 that can be <1>
R2C1 can only be <2>
R5C1 can only be <1>
R5C3 can only be <2>
R3C3 is the only square in row 3 that can be <1>
Intersection of row 2 with block 2. The value <4> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <4> from <469> leaving <69>
R3C5 - removing <4> from <479> leaving <79>
Squares R3C5 and R3C7 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <9> from <459> leaving <45>
R3C8 - removing <79> from <4579> leaving <45>
Intersection of column 8 with block 6. The values <17> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R5C7 - removing <7> from <6789> leaving <689>
Squares R2C3 and R2C9 in row 2 and R8C3 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 9 can be removed.
R7C3 - removing <5> from <56> leaving <6>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 8 can be removed.
R2C5 - removing <6> from <4679> leaving <479>
R5C8 - removing <6> from <6789> leaving <789>
R8C5 - removing <6> from <3468> leaving <348>
Squares R3C5, R3C7, R2C5 and R2C7 form a Type-3 Unique Rectangle on <79>. Upon close inspection, it is clear that:
(R2C5 or R2C7)<46> and R2C4<46> form a naked pair on <46> in row 2. No other squares in the row can contain these possibilities
R2C9 - removing <6> from <569> leaving <59>
Squares R2C3 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C5 - removing <9> from <479> leaving <47>
R2C7 - removing <9> from <679> leaving <67>
Squares R9C5 (XY), R9C2 (XZ) and R1C5 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R1C2 - removing <9> from <49> leaving <4>
R3C2 can only be <5>
R3C8 can only be <4>
R7C2 can only be <2>
R2C3 can only be <9>
R9C2 can only be <9>
R9C8 can only be <6>
R8C3 can only be <5>
R9C5 can only be <2>
R1C8 can only be <9>
R1C5 can only be <6>
R2C9 can only be <5>
R3C7 can only be <7>
R8C9 can only be <9>
R3C5 can only be <9>
R2C7 can only be <6>
R5C9 can only be <6>
R2C4 can only be <4>
R2C5 can only be <7>
R5C4 can only be <8>
R5C7 can only be <9>
R5C8 can only be <7>
R8C4 can only be <6>
R6C5 can only be <1>
R5C2 can only be <3>
R4C8 can only be <1>
R6C8 can only be <8>
R4C5 can only be <3>
R7C8 can only be <5>
R4C2 can only be <7>
R7C5 can only be <8>
R5C6 can only be <4>
R8C6 can only be <3>
R7C7 can only be <3>
R8C5 can only be <4>
R8C7 can only be <8>
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