Mar 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C1 can only be <9>
R2C1 is the only square in row 2 that can be <6>
R4C4 is the only square in row 4 that can be <6>
R8C1 is the only square in row 8 that can be <5>
R9C7 is the only square in row 9 that can be <6>
R1C1 is the only square in column 1 that can be <7>
R1C2 is the only square in row 1 that can be <2>
R4C1 is the only square in column 1 that can be <2>
R5C3 is the only square in column 3 that can be <9>
Squares R7C5 and R9C4 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <1> from <129> leaving <29>
R9C6 - removing <1> from <129> leaving <29>
Squares R1C7<38>, R2C8<47>, R2C9<347> and R3C9<348> in block 3 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <48> from <4589> leaving <59>
R1C9 - removing <348> from <34589> leaving <59>
Squares R3C5 and R3C9 in row 3 and R4C5 and R4C9 in row 4 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 5 and 9 can be removed.
R5C5 - removing <8> from <23478> leaving <2347>
R6C5 - removing <8> from <1348> leaving <134>
R6C9 - removing <8> from <3458> leaving <345>
R8C9 - removing <8> from <1289> leaving <129>
R9C9 - removing <8> from <12789> leaving <1279>
Intersection of block 9 with column 8. The value <8> only appears in one or more of squares R7C8, R8C8 and R9C8 of block 9. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R5C8 - removing <8> from <458> leaving <45>
Squares R2C2 and R2C5 in row 2, R7C5 and R7C9 in row 7 and R8C2 and R8C9 in row 8 form a Swordfish pattern on possibility <1>. All other instances of this possibility in columns 2, 5 and 9 can be removed.
R6C5 - removing <1> from <134> leaving <34>
R9C2 - removing <1> from <1348> leaving <348>
R9C9 - removing <1> from <1279> leaving <279>
Squares R8C2 (XY), R9C3 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R9C2 - removing <4> from <348> leaving <38>
Squares R2C2 and R5C2 in column 2 and R2C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C5 - removing <4> from <134> leaving <13>
R5C5 - removing <4> from <2347> leaving <237>
R5C6 - removing <4> from <234> leaving <23>
R2C9 - removing <4> from <347> leaving <37>
Squares R1C4 (XY), R2C5 (XZ) and R1C7 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R1C6 - removing <3> from <134> leaving <14>
R2C9 - removing <3> from <37> leaving <7>
R2C8 can only be <4>
R7C9 can only be <1>
R7C5 can only be <7>
R5C8 can only be <5>
R1C8 can only be <9>
R9C4 can only be <1>
R9C3 can only be <4>
R1C4 can only be <8>
R1C7 can only be <3>
R5C4 can only be <7>
R6C4 can only be <5>
R5C7 can only be <8>
R3C9 can only be <8>
R1C9 can only be <5>
R8C8 can only be <8>
R4C9 can only be <4>
R4C6 can only be <9>
R6C9 can only be <3>
R5C2 can only be <4>
R6C5 can only be <4>
R8C2 can only be <1>
R9C8 can only be <7>
R1C3 can only be <1>
R1C6 can only be <4>
R2C2 can only be <3>
R6C6 can only be <1>
R3C5 can only be <3>
R2C5 can only be <1>
R9C2 can only be <8>
R3C1 can only be <4>
R6C1 can only be <8>
R5C5 can only be <2>
R4C5 can only be <8>
R9C6 can only be <2>
R5C6 can only be <3>
R8C5 can only be <9>
R9C1 can only be <3>
R8C9 can only be <2>
R9C9 can only be <9>
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