Sep 29 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C5 can only be <5>
R8C4 can only be <3>
R8C6 can only be <1>
R2C4 can only be <6>
R7C5 can only be <9>
R8C1 can only be <2>
R5C4 can only be <5>
R5C7 is the only square in row 5 that can be <1>
R9C1 is the only square in column 1 that can be <4>
R9C2 is the only square in row 9 that can be <1>
R3C8 is the only square in row 3 that can be <1>
R1C1 is the only square in row 1 that can be <1>
Squares R5C6 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <3> from <367> leaving <67>
R5C5 - removing <23> from <2367> leaving <67>
Squares R9C8 and R9C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <7> from <5679> leaving <569>
R8C9 - removing <7> from <6789> leaving <689>
Squares R2C1 and R5C1 in column 1 and R2C6 and R5C6 in column 6 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C2 - removing <3> from <23589> leaving <2589>
R2C3 - removing <3> from <238> leaving <28>
R5C3 - removing <3> from <237> leaving <27>
R7C3 is the only square in column 3 that can be <3>
Squares R9C8, R9C9, R2C8 and R2C9 form a Type-4 Unique Rectangle on <27>.
R2C8 - removing <2> from <24579> leaving <4579>
R2C9 - removing <2> from <2789> leaving <789>
Intersection of block 3 with row 1. The value <2> only appears in one or more of squares R1C7, R1C8 and R1C9 of block 3. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C2 - removing <2> from <2389> leaving <389>
R1C5 - removing <2> from <238> leaving <38>
Squares R2C6 (XY), R2C3 (XZ) and R1C5 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R1C2 - removing <8> from <389> leaving <39>
Squares R1C2 and R2C1 in block 1 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 block.
R2C2 - removing <9> from <2589> leaving <258>
Squares R5C3 (XY), R5C6 (XZ) and R4C2 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R5C1 - removing <3> from <39> leaving <9>
R5C9 can only be <6>
R2C1 can only be <3>
R5C5 can only be <7>
R4C8 can only be <3>
R2C6 can only be <2>
R1C2 can only be <9>
R2C3 can only be <8>
R5C6 can only be <3>
R3C5 can only be <8>
R3C7 can only be <5>
R1C5 can only be <3>
R4C2 can only be <7>
R6C8 can only be <9>
R5C3 can only be <2>
R4C5 can only be <6>
R6C5 can only be <2>
R6C2 can only be <3>
R1C8 can only be <2>
R1C9 can only be <8>
R9C8 can only be <7>
R8C9 can only be <9>
R2C2 can only be <5>
R3C3 can only be <6>
R8C7 can only be <8>
R2C9 can only be <7>
R9C9 can only be <2>
R2C8 can only be <4>
R2C7 can only be <9>
R7C8 can only be <6>
R3C2 can only be <2>
R8C3 can only be <7>
R7C2 can only be <8>
R8C8 can only be <5>
R8C2 can only be <6>
R7C7 can only be <4>
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