Sep 08 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C2 can only be <2>
R8C6 can only be <4>
R4C7 is the only square in row 4 that can be <2>
R4C8 is the only square in row 4 that can be <3>
R8C8 can only be <7>
R4C6 is the only square in row 4 that can be <1>
R7C6 can only be <6>
R5C5 can only be <6>
R1C5 can only be <1>
R6C4 can only be <4>
R3C7 is the only square in row 3 that can be <1>
R7C4 is the only square in row 7 that can be <1>
R7C9 is the only square in column 9 that can be <5>
R9C5 is the only square in column 5 that can be <5>
R3C9 is the only square in column 9 that can be <4>
R1C2 is the only square in row 1 that can be <4>
Squares R7C1 and R9C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <89> from <2389> leaving <23>
R8C1 - removing <9> from <59> leaving <5>
R8C3 - removing <9> from <2359> leaving <235>
R4C2 is the only square in row 4 that can be <5>
R2C3 is the only square in row 2 that can be <5>
Squares R7C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C3 - removing <3> from <36789> leaving <6789>
Intersection of column 8 with block 9. The value <8> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <8> from <3489> leaving <349>
R9C7 - removing <8> from <689> leaving <69>
Squares R2C6, R3C6, R2C2 and R3C2 form a Type-2 Unique Rectangle on <38>.
R6C2 - removing <9> from <89> leaving <8>
R3C1 - removing <9> from <6789> leaving <678>
R3C3 - removing <9> from <6789> leaving <678>
Squares R4C1, R4C9, R6C1 and R6C9 form a Type-2 Unique Rectangle on <69>.
R6C3 - removing <7> from <1679> leaving <169>
Squares R9C3 (XY), R1C3 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R1C7 - removing <6> from <68> leaving <8>
R1C3 can only be <6>
R2C6 is the only square in row 2 that can be <8>
R3C6 can only be <3>
R3C2 can only be <9>
R3C5 can only be <2>
R2C2 can only be <3>
R3C4 can only be <6>
R7C5 can only be <9>
R7C1 can only be <8>
R8C4 can only be <2>
R8C3 can only be <3>
R2C4 can only be <9>
R7C8 can only be <4>
R3C1 can only be <7>
R9C3 can only be <9>
R7C7 can only be <3>
R5C8 can only be <1>
R8C7 can only be <9>
R7C3 can only be <2>
R9C7 can only be <6>
R6C3 can only be <1>
R9C8 can only be <8>
R2C7 can only be <7>
R2C9 can only be <6>
R5C7 can only be <4>
R4C9 can only be <9>
R3C3 can only be <8>
R4C1 can only be <6>
R6C9 can only be <7>
R5C3 can only be <7>
R6C8 can only be <6>
R6C1 can only be <9>
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