Aug 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 can only be <7>
R5C1 can only be <4>
R8C1 can only be <6>
R2C3 is the only square in row 2 that can be <9>
R8C3 can only be <3>
R9C3 can only be <7>
R4C3 can only be <6>
R6C3 can only be <5>
R7C2 can only be <4>
R6C7 can only be <7>
R5C3 can only be <8>
R6C5 can only be <4>
R4C7 can only be <2>
R9C2 can only be <9>
R4C5 can only be <7>
R5C2 can only be <7>
R1C3 can only be <1>
R5C5 can only be <2>
R5C7 is the only square in row 5 that can be <1>
R8C6 is the only square in row 8 that can be <9>
Squares R2C5 and R2C7 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C6 - removing <58> from <2458> leaving <24>
R2C9 - removing <5> from <235> leaving <23>
Squares R2C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C5 - removing <58> from <1568> leaving <16>
R7C5 - removing <5> from <156> leaving <16>
Squares R2C5 and R2C7 in row 2 and R8C5 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 5 and 7 can be removed.
R1C7 - removing <8> from <568> leaving <56>
R9C7 - removing <8> from <468> leaving <46>
Squares R3C5, R7C5, R3C4 and R7C4 form a Type-4 Unique Rectangle on <16>.
R3C4 - removing <6> from <126> leaving <12>
R7C4 - removing <6> from <167> leaving <17>
Squares R3C5 and R3C8 in row 3 and R7C5 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 8 can be removed.
R1C8 - removing <6> from <3568> leaving <358>
R9C8 - removing <6> from <268> leaving <28>
Squares R8C9 (XY), R9C8 (XZ) and R8C5 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R8C7 - removing <8> from <458> leaving <45>
R9C6 - removing <8> from <248> leaving <24>
R8C5 is the only square in row 8 that can be <8>
R2C5 can only be <5>
R2C7 can only be <8>
R9C8 is the only square in row 9 that can be <8>
R7C6 is the only square in column 6 that can be <5>
R7C8 can only be <6>
R7C5 can only be <1>
R9C7 can only be <4>
R9C6 can only be <2>
R8C7 can only be <5>
R7C4 can only be <7>
R3C5 can only be <6>
R8C9 can only be <2>
R1C7 can only be <6>
R8C4 can only be <4>
R2C9 can only be <3>
R9C4 can only be <6>
R2C6 can only be <4>
R3C6 can only be <8>
R2C4 can only be <2>
R5C9 can only be <5>
R1C8 can only be <5>
R3C2 can only be <5>
R1C6 can only be <7>
R5C8 can only be <3>
R1C4 can only be <3>
R1C2 can only be <8>
R3C8 can only be <2>
R3C4 can only be <1>
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