Dec 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 can only be <9>
R5C2 can only be <8>
R4C2 can only be <5>
R8C2 can only be <4>
R2C2 can only be <6>
R5C3 is the only square in row 5 that can be <2>
R9C3 can only be <8>
R7C3 can only be <6>
R5C8 is the only square in row 5 that can be <3>
R6C9 is the only square in row 6 that can be <6>
R4C4 is the only square in row 4 that can be <6>
R1C5 is the only square in row 1 that can be <6>
R4C9 is the only square in row 4 that can be <9>
R7C5 is the only square in row 7 that can be <3>
R8C5 is the only square in row 8 that can be <9>
R8C1 is the only square in row 8 that can be <5>
R7C1 can only be <2>
R7C7 is the only square in column 7 that can be <5>
Squares R8C8 and R8C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <8> from <148> leaving <14>
R9C9 - removing <2> from <124> leaving <14>
Squares R7C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C9 - removing <4> from <2478> leaving <278>
R3C9 - removing <14> from <1478> leaving <78>
R3C7 is the only square in row 3 that can be <1>
Intersection of column 9 with block 3. The value <7> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <7> from <478> leaving <48>
Squares R8C8, R8C9, R2C8 and R2C9 form a Type-3 Unique Rectangle on <28>. Upon close inspection, it is clear that:
(R2C8 or R2C9)<47> and R2C5<47> form a naked pair on <47> in row 2. No other squares in the row can contain these possibilities
R2C1 - removing <47> from <478> leaving <8>
Squares R3C3, R6C3, R3C1 and R6C1 form a Type-4 Unique Rectangle on <37>.
R3C1 - removing <7> from <347> leaving <34>
R6C1 - removing <7> from <137> leaving <13>
Squares R1C7 (XY), R1C1 (XZ) and R4C7 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R4C1 - removing <7> from <17> leaving <1>
R4C8 can only be <8>
R6C1 can only be <3>
R4C7 can only be <7>
R8C8 can only be <2>
R6C3 can only be <7>
R3C1 can only be <4>
R6C6 can only be <4>
R3C3 can only be <3>
R6C8 can only be <1>
R7C6 can only be <8>
R8C9 can only be <8>
R2C8 can only be <4>
R3C9 can only be <7>
R2C5 can only be <7>
R1C7 can only be <8>
R1C1 can only be <7>
R3C5 can only be <5>
R2C9 can only be <2>
R5C7 can only be <4>
R1C6 can only be <2>
R9C6 can only be <5>
R1C4 can only be <4>
R5C5 can only be <1>
R3C6 can only be <9>
R3C4 can only be <8>
R5C6 can only be <7>
R5C4 can only be <9>
R9C5 can only be <4>
R9C9 can only be <1>
R7C4 can only be <1>
R9C4 can only be <2>
R7C9 can only be <4>
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