Aug 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C9 can only be <4>
R6C7 can only be <9>
R6C6 can only be <2>
R4C8 can only be <5>
R5C9 can only be <1>
R5C8 can only be <6>
R1C7 is the only square in row 1 that can be <8>
R2C2 is the only square in row 2 that can be <5>
R8C2 is the only square in row 8 that can be <8>
R6C2 can only be <3>
R6C5 can only be <8>
R4C5 is the only square in row 4 that can be <3>
R4C3 is the only square in row 4 that can be <4>
R5C1 is the only square in row 5 that can be <8>
R7C9 is the only square in row 7 that can be <3>
R9C5 is the only square in row 9 that can be <1>
R9C9 is the only square in row 9 that can be <5>
R8C5 is the only square in row 8 that can be <5>
R5C4 is the only square in row 5 that can be <5>
R8C7 is the only square in row 8 that can be <6>
R9C1 is the only square in column 1 that can be <2>
R9C3 is the only square in row 9 that can be <3>
R9C2 is the only square in row 9 that can be <6>
R7C5 is the only square in row 7 that can be <6>
R1C2 is the only square in column 2 that can be <4>
R5C6 is the only square in column 6 that can be <4>
Squares R2C1 and R4C1 in column 1 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 column.
R1C1 - removing <79> from <3679> leaving <36>
R3C1 - removing <7> from <367> leaving <36>
Intersection of row 3 with block 2. The value <7> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C4 - removing <7> from <679> leaving <69>
R1C5 - removing <7> from <279> leaving <29>
R2C5 - removing <7> from <2479> leaving <249>
Squares R1C3 and R1C9 in row 1 and R8C3 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 9 can be removed.
R2C3 - removing <7> from <179> leaving <19>
Squares R2C1 and R5C5 form a remote naked pair. <79> can be removed from any square that is common to their groups.
R2C5 - removing <9> from <249> leaving <24>
Intersection of row 2 with block 1. The value <9> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <9> from <179> leaving <17>
Squares R2C7 (XY), R2C5 (XZ) and R1C9 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R1C5 - removing <2> from <29> leaving <9>
R2C8 - removing <2> from <124> leaving <14>
R1C4 can only be <6>
R5C5 can only be <7>
R5C2 can only be <9>
R3C5 can only be <4>
R4C4 can only be <9>
R1C1 can only be <3>
R3C4 can only be <7>
R3C8 can only be <3>
R2C5 can only be <2>
R3C1 can only be <6>
R4C1 can only be <7>
R7C2 can only be <7>
R7C6 can only be <9>
R8C3 can only be <9>
R9C6 can only be <7>
R8C8 can only be <2>
R2C3 can only be <1>
R8C9 can only be <7>
R1C8 can only be <1>
R1C9 can only be <2>
R9C7 can only be <4>
R9C8 can only be <9>
R2C7 can only be <7>
R1C3 can only be <7>
R2C8 can only be <4>
R2C1 can only be <9>
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