Aug 30 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C6 can only be <5>
R8C9 can only be <6>
R9C8 can only be <4>
R7C3 can only be <4>
R2C9 can only be <5>
R7C7 can only be <8>
R9C9 can only be <2>
R1C1 is the only square in column 1 that can be <4>
Squares R4C3 and R6C3 in column 3 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 column.
R5C3 - removing <23> from <2357> leaving <57>
Squares R1C9 and R6C9 in column 9 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 column.
R4C9 - removing <39> from <3489> leaving <48>
R5C9 - removing <39> from <3489> leaving <48>
Squares R1C2 and R5C2 in column 2 and R1C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 5 can be removed.
R5C1 - removing <6> from <56789> leaving <5789>
R1C4 - removing <6> from <689> leaving <89>
R1C5 - removing <6> from <25689> leaving <2589>
R5C7 - removing <6> from <1269> leaving <129>
Squares R1C4 and R9C4 in column 4 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.
R3C4 - removing <9> from <469> leaving <46>
R5C4 - removing <9> from <349> leaving <34>
Squares R2C1 and R2C5 in row 2 and R8C1 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 5 can be removed.
R3C5 - removing <7> from <45679> leaving <4569>
R5C1 - removing <7> from <5789> leaving <589>
R9C1 - removing <7> from <157> leaving <15>
R9C5 - removing <7> from <1789> leaving <189>
Squares R1C4, R9C4, R1C5 and R9C5 form a Type-4 Unique Rectangle on <89>.
R1C5 - removing <9> from <2589> leaving <258>
R9C5 - removing <9> from <189> leaving <18>
Squares R1C2 (XY), R9C2 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R8C1 - removing <7> from <17> leaving <1>
R8C5 can only be <7>
R9C1 can only be <5>
R2C5 can only be <6>
R9C2 can only be <7>
R2C1 can only be <7>
R7C5 can only be <3>
R3C4 can only be <4>
R5C4 can only be <3>
R5C8 can only be <6>
R7C4 can only be <6>
R5C2 can only be <5>
R1C8 can only be <3>
R1C9 can only be <9>
R1C4 can only be <8>
R1C6 can only be <2>
R6C9 can only be <3>
R3C7 can only be <6>
R3C3 can only be <5>
R3C5 can only be <9>
R5C3 can only be <7>
R1C2 can only be <6>
R3C6 can only be <7>
R6C3 can only be <2>
R9C4 can only be <9>
R1C5 can only be <5>
R6C5 can only be <1>
R4C3 can only be <3>
R6C7 can only be <9>
R9C5 can only be <8>
R5C6 can only be <9>
R6C1 can only be <6>
R4C7 can only be <2>
R9C6 can only be <1>
R4C5 can only be <4>
R5C7 can only be <1>
R5C1 can only be <8>
R4C9 can only be <8>
R5C5 can only be <2>
R4C1 can only be <9>
R5C9 can only be <4>
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