Mar 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C7 is the only square in row 7 that can be <4>
R7C5 is the only square in row 7 that can be <2>
R6C4 is the only square in row 6 that can be <2>
R7C8 is the only square in row 7 that can be <6>
R9C9 is the only square in row 9 that can be <2>
R9C1 is the only square in column 1 that can be <7>
R9C3 is the only square in row 9 that can be <1>
R6C6 is the only square in row 6 that can be <1>
R8C4 is the only square in row 8 that can be <1>
R1C7 is the only square in column 7 that can be <2>
R5C9 is the only square in column 9 that can be <9>
R9C5 is the only square in block 8 that can be <3>
R9C8 can only be <8>
R8C7 can only be <7>
R4C4 is the only square in row 4 that can be <3>
Squares R8C8 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <3> from <389> leaving <89>
Squares R7C6 and R8C6 in column 6 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 column.
R2C6 - removing <9> from <679> leaving <67>
R4C6 - removing <89> from <489> leaving <4>
R5C6 - removing <8> from <4678> leaving <467>
R4C5 is the only square in row 4 that can be <9>
Squares R1C1 and R4C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C1 - removing <18> from <1248> leaving <24>
Intersection of row 1 with block 1. The value <1> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <1> from <1589> leaving <589>
Squares R1C5 and R1C9 in row 1 and R6C5 and R6C9 in row 6 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 9 can be removed.
R3C5 - removing <6> from <5678> leaving <578>
R5C5 - removing <6> from <5678> leaving <578>
Squares R8C2, R8C6, R7C2 and R7C6 form a Type-1 Unique Rectangle on <89>.
R7C2 - removing <89> from <389> leaving <3>
Squares R2C8 (XY), R1C9 (XZ) and R2C6 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R1C5 - removing <6> from <568> leaving <58>
R1C9 is the only square in row 1 that can be <6>
R6C9 can only be <3>
R3C7 can only be <1>
R4C7 can only be <8>
R4C1 can only be <1>
R5C7 can only be <6>
R5C6 can only be <7>
R6C3 can only be <8>
R8C9 can only be <5>
R5C8 can only be <1>
R8C8 can only be <3>
R1C1 can only be <8>
R2C6 can only be <6>
R6C5 can only be <6>
R7C3 can only be <9>
R5C2 can only be <2>
R7C6 can only be <8>
R3C3 can only be <6>
R8C2 can only be <8>
R8C6 can only be <9>
R1C5 can only be <5>
R1C2 can only be <1>
R5C5 can only be <8>
R2C4 can only be <9>
R3C4 can only be <8>
R2C3 can only be <4>
R3C5 can only be <7>
R5C4 can only be <5>
R3C8 can only be <5>
R3C2 can only be <9>
R2C8 can only be <7>
R5C1 can only be <4>
R2C2 can only be <5>
R2C1 can only be <2>
R5C3 can only be <3>
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