Sep 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C1 can only be <8>
R5C7 can only be <3>
R3C8 is the only square in row 3 that can be <7>
R4C4 is the only square in row 4 that can be <3>
R6C5 is the only square in row 6 that can be <8>
R7C2 is the only square in row 7 that can be <7>
R4C6 is the only square in row 4 that can be <7>
R5C3 is the only square in row 5 that can be <7>
R8C2 is the only square in row 8 that can be <2>
R9C7 is the only square in row 9 that can be <7>
R8C4 is the only square in row 8 that can be <7>
R2C3 is the only square in column 3 that can be <5>
R8C7 is the only square in column 7 that can be <9>
R8C3 can only be <1>
R1C3 can only be <3>
R9C3 can only be <9>
R9C2 is the only square in column 2 that can be <3>
R7C5 is the only square in block 8 that can be <5>
Squares R8C1 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <46> from <4568> leaving <58>
R8C9 - removing <4> from <458> leaving <58>
Squares R7C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <46> from <1469> leaving <19>
R3C1 - removing <4> from <149> leaving <19>
Squares R4C2 and R6C2 in column 2 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.
R1C2 - removing <1> from <146> leaving <46>
R2C2 - removing <1> from <1468> leaving <468>
R3C2 - removing <1> from <148> leaving <48>
Squares R3C2 and R3C9 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C5 - removing <4> from <149> leaving <19>
Squares R3C5 and R4C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <1> from <124> leaving <24>
R1C7 is the only square in row 1 that can be <1>
R2C7 can only be <6>
R1C2 is the only square in row 1 that can be <6>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 8 can be removed.
R2C8 - removing <4> from <2348> leaving <238>
R5C5 - removing <4> from <246> leaving <26>
R7C8 - removing <4> from <346> leaving <36>
Squares R3C2, R3C9, R2C2 and R2C9 form a Type-1 Unique Rectangle on <48>.
R2C9 - removing <48> from <2348> leaving <23>
Squares R2C9 (XY), R1C8 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C9 - removing <4> from <48> leaving <8>
R9C8 - removing <4> from <46> leaving <6>
R3C2 can only be <4>
R8C9 can only be <5>
R8C8 can only be <8>
R5C9 can only be <2>
R9C5 can only be <4>
R7C8 can only be <3>
R2C2 can only be <8>
R5C5 can only be <6>
R2C9 can only be <3>
R7C9 can only be <4>
R2C8 can only be <2>
R7C1 can only be <6>
R1C5 can only be <2>
R8C6 can only be <6>
R1C8 can only be <4>
R5C6 can only be <4>
R5C4 can only be <5>
R2C6 can only be <1>
R8C1 can only be <4>
R2C1 can only be <9>
R6C6 can only be <2>
R3C5 can only be <9>
R3C1 can only be <1>
R4C5 can only be <1>
R2C4 can only be <4>
R4C2 can only be <5>
R6C4 can only be <9>
R6C8 can only be <5>
R6C2 can only be <1>
R4C8 can only be <9>
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