Jan 18 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 can only be <5>
R6C7 can only be <6>
R3C7 is the only square in row 3 that can be <3>
R5C3 is the only square in row 5 that can be <7>
R1C7 is the only square in column 7 that can be <8>
R1C9 is the only square in row 1 that can be <5>
Squares R1C1 and R2C3 in block 1 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 block.
R1C3 - removing <49> from <249> leaving <2>
R3C1 - removing <49> from <4689> leaving <68>
R3C2 - removing <9> from <169> leaving <16>
R3C3 - removing <49> from <124689> leaving <1268>
R3C5 is the only square in row 3 that can be <2>
Squares R4C3 and R5C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C1 - removing <69> from <3469> leaving <34>
Squares R4C7 and R5C8 in block 6 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 block.
R5C7 - removing <59> from <1259> leaving <12>
R5C9 - removing <9> from <129> leaving <12>
Intersection of row 3 with block 3. The value <9> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <9> from <479> leaving <47>
Squares R5C6 and R7C6 in column 6 and R5C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 7 can be removed.
R7C3 - removing <5> from <135689> leaving <13689>
R5C5 - removing <5> from <34568> leaving <3468>
R7C5 - removing <5> from <15678> leaving <1678>
R7C7 - removing <5> from <124579> leaving <12479>
Squares R4C3 and R4C5 in row 4 and R8C3 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.
R3C3 - removing <6> from <168> leaving <18>
R5C5 - removing <6> from <3468> leaving <348>
R7C3 - removing <6> from <13689> leaving <1389>
R7C5 - removing <6> from <1678> leaving <178>
Squares R5C7, R5C9, R7C7 and R7C9 form a Type-4 Unique Rectangle on <12>.
R7C7 - removing <1> from <12479> leaving <2479>
R7C9 - removing <1> from <1279> leaving <279>
Squares R5C8 (XY), R5C6 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C6 - removing <4> from <47> leaving <7>
R3C9 can only be <9>
R7C6 can only be <5>
R3C8 can only be <4>
R5C6 can only be <4>
R7C8 can only be <9>
R2C7 can only be <7>
R5C1 can only be <3>
R6C5 can only be <3>
R6C3 can only be <4>
R5C5 can only be <8>
R5C8 can only be <5>
R5C4 can only be <6>
R4C7 can only be <9>
R2C3 can only be <9>
R2C5 can only be <4>
R4C3 can only be <6>
R1C1 can only be <4>
R1C5 can only be <9>
R4C5 can only be <5>
R5C2 can only be <9>
R7C4 can only be <8>
R7C1 can only be <6>
R7C2 can only be <1>
R3C1 can only be <8>
R7C3 can only be <3>
R7C5 can only be <7>
R3C2 can only be <6>
R8C3 can only be <5>
R7C9 can only be <2>
R9C5 can only be <1>
R7C7 can only be <4>
R5C9 can only be <1>
R8C7 can only be <1>
R9C3 can only be <8>
R8C5 can only be <6>
R5C7 can only be <2>
R9C7 can only be <5>
R9C9 can only be <7>
R9C1 can only be <9>
R3C3 can only be <1>
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