Aug 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 is the only square in row 1 that can be <2>
R3C2 is the only square in row 3 that can be <8>
R3C6 is the only square in row 3 that can be <3>
R9C3 is the only square in row 9 that can be <2>
R4C9 is the only square in row 4 that can be <2>
R6C2 is the only square in row 6 that can be <2>
R1C3 is the only square in column 3 that can be <6>
R7C5 is the only square in column 5 that can be <7>
R6C9 is the only square in column 9 that can be <3>
R4C4 is the only square in column 4 that can be <3>
R3C9 is the only square in column 9 that can be <6>
R1C7 is the only square in block 3 that can be <7>
Squares R7C1 and R7C3 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C4 - removing <9> from <569> leaving <56>
R7C8 - removing <3> from <356> leaving <56>
R8C8 is the only square in column 8 that can be <3>
R8C1 is the only square in row 8 that can be <7>
R8C4 is the only square in row 8 that can be <8>
R9C8 is the only square in row 9 that can be <7>
R9C1 is the only square in row 9 that can be <8>
R6C1 can only be <5>
Squares R6C4 and R6C6 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C7 - removing <6> from <468> leaving <48>
Squares R1C4 and R3C5 in block 2 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.
R2C4 - removing <59> from <4579> leaving <47>
R2C6 - removing <59> from <4579> leaving <47>
Squares R6C4 and R6C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C6 - removing <6> from <569> leaving <59>
Intersection of column 8 with block 6. The value <1> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <1> from <1568> leaving <568>
R5C7 - removing <1> from <145> leaving <45>
R9C7 is the only square in column 7 that can be <1>
Squares R3C7 and R4C6 form a remote naked pair. <59> can be removed from any square that is common to their groups.
R4C7 - removing <5> from <568> leaving <68>
Squares R3C5 and R5C5 in column 5 and R3C7 and R5C7 in column 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 3 and 5 can be removed.
R5C8 - removing <5> from <15> leaving <1>
Squares R7C4 (XY), R1C4 (XZ) and R8C6 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R9C4 - removing <9> from <459> leaving <45>
R1C4 is the only square in column 4 that can be <9>
R3C5 can only be <5>
R3C7 can only be <9>
R5C5 can only be <9>
R8C7 can only be <6>
R5C2 can only be <3>
R4C6 can only be <5>
R8C6 can only be <9>
R4C7 can only be <8>
R7C8 can only be <5>
R4C8 can only be <6>
R6C7 can only be <4>
R5C3 can only be <4>
R1C2 can only be <5>
R5C7 can only be <5>
R6C3 can only be <8>
R7C4 can only be <6>
R9C9 can only be <9>
R9C6 can only be <4>
R9C4 can only be <5>
R2C6 can only be <7>
R1C9 can only be <1>
R2C2 can only be <9>
R1C1 can only be <3>
R2C9 can only be <5>
R2C3 can only be <1>
R4C3 can only be <9>
R2C4 can only be <4>
R6C6 can only be <6>
R4C1 can only be <1>
R7C3 can only be <3>
R6C4 can only be <7>
R7C1 can only be <9>
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