Mar 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C1 can only be <5>
R9C7 can only be <3>
R9C1 can only be <1>
R9C3 can only be <7>
R8C2 can only be <8>
R9C9 can only be <5>
R4C1 is the only square in row 4 that can be <4>
R4C8 is the only square in row 4 that can be <2>
R4C9 is the only square in row 4 that can be <7>
R7C9 can only be <9>
R7C5 can only be <7>
R8C8 can only be <7>
R2C4 is the only square in row 2 that can be <7>
R6C1 is the only square in row 6 that can be <2>
Squares R1C1 and R3C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C2 - removing <6> from <356> leaving <35>
Intersection of row 2 with block 2. The value <6> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. 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 <6> from <156> leaving <15>
R1C6 - removing <6> from <1689> leaving <189>
R3C5 - removing <6> from <689> leaving <89>
Squares R1C4 and R8C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C4 - removing <1> from <126> leaving <26>
Squares R3C5 and R3C9 in row 3 and R6C5 and R6C9 in row 6 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 5 and 9 can be removed.
R1C9 - removing <8> from <368> leaving <36>
R5C5 - removing <8> from <1368> leaving <136>
Squares R9C4, R9C6, R5C4 and R5C6 form a Type-1 Unique Rectangle on <26>.
R5C6 - removing <26> from <1268> leaving <18>
R5C4 is the only square in row 5 that can be <2>
R9C4 can only be <6>
R9C6 can only be <2>
R2C6 is the only square in column 6 that can be <6>
Squares R1C7 (XY), R3C9 (XZ) and R1C1 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R1C9 - removing <6> from <36> leaving <3>
R3C1 - removing <6> from <69> leaving <9>
R1C3 can only be <5>
R6C9 can only be <8>
R2C8 can only be <9>
R2C5 can only be <5>
R1C7 can only be <8>
R3C5 can only be <8>
R1C1 can only be <6>
R3C9 can only be <6>
R5C7 can only be <9>
R1C4 can only be <1>
R5C3 can only be <3>
R2C2 can only be <3>
R1C6 can only be <9>
R8C4 can only be <5>
R8C6 can only be <1>
R4C2 can only be <1>
R4C5 can only be <3>
R6C2 can only be <6>
R5C8 can only be <1>
R5C5 can only be <6>
R5C6 can only be <8>
R6C8 can only be <3>
R6C5 can only be <1>
R5C2 can only be <5>
R8C5 can only be <9>
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