Jun 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <2>
R4C4 can only be <8>
R4C6 can only be <9>
R5C1 can only be <1>
R5C6 can only be <2>
R5C9 can only be <5>
R6C4 can only be <1>
R6C5 can only be <5>
R6C6 can only be <6>
R8C2 can only be <3>
R9C5 can only be <8>
R4C5 can only be <7>
R5C4 can only be <3>
R5C5 can only be <4>
R8C8 can only be <1>
R9C3 can only be <5>
R2C2 is the only square in row 2 that can be <5>
R3C7 is the only square in row 3 that can be <4>
R9C1 is the only square in row 9 that can be <4>
Squares R9C2 and R9C7 in row 9 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.
R9C8 - removing <6> from <369> leaving <39>
R9C9 - removing <7> from <379> leaving <39>
Squares R7C3 and R8C1 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <28> from <2678> leaving <67>
Intersection of column 8 with block 3. The value <6> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <6> from <678> leaving <78>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C1 - removing <8> from <3678> leaving <367>
R1C9 - removing <8> from <13789> leaving <1379>
R7C9 - removing <8> from <278> leaving <27>
Squares R9C8, R9C9, R1C8 and R1C9 form a Type-3 Unique Rectangle on <39>. Upon close inspection, it is clear that:
(R1C8 or R1C9)<167>, R1C7<78>, R1C3<18> and R1C2<67> form a naked quad on <1678> in row 1. No other squares in the row can contain these possibilities
R1C1 - removing <67> from <367> leaving <3>
Squares R1C2 (XY), R2C1 (XZ) and R1C7 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R1C3 - removing <8> from <18> leaving <1>
R2C9 - removing <8> from <38> leaving <3>
R3C3 can only be <2>
R2C8 can only be <6>
R9C9 can only be <9>
R3C1 can only be <7>
R7C3 can only be <8>
R8C1 can only be <2>
R8C9 can only be <8>
R9C8 can only be <3>
R1C9 can only be <7>
R1C2 can only be <6>
R1C7 can only be <8>
R3C9 can only be <1>
R7C9 can only be <2>
R2C1 can only be <8>
R1C8 can only be <9>
R7C1 can only be <6>
R7C7 can only be <7>
R9C2 can only be <7>
R9C7 can only be <6>
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