Jan 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C2 can only be <1>
R8C2 can only be <2>
R9C5 can only be <3>
R2C7 is the only square in row 2 that can be <6>
R4C6 is the only square in row 4 that can be <6>
R4C3 is the only square in row 4 that can be <3>
R5C2 can only be <8>
R5C1 can only be <9>
R3C2 can only be <3>
R7C2 can only be <6>
R6C3 can only be <5>
R6C6 can only be <7>
R6C7 can only be <2>
R6C4 can only be <9>
R6C5 can only be <8>
R5C6 is the only square in row 5 that can be <3>
R7C8 is the only square in row 7 that can be <2>
R7C7 is the only square in row 7 that can be <3>
Squares R8C7 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C5 - removing <5> from <457> leaving <47>
Squares R2C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C8 - removing <59> from <1459> leaving <14>
R5C8 - removing <5> from <145> leaving <14>
Squares R8C7 and R8C8 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <5> from <158> leaving <18>
Squares R2C3 and R2C5 in row 2 and R8C3 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 5 can be removed.
R3C3 - removing <7> from <2789> leaving <289>
R7C3 - removing <7> from <1478> leaving <148>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <8> from <289> leaving <29>
R3C7 - removing <8> from <14589> leaving <1459>
R7C3 - removing <8> from <148> leaving <14>
Squares R1C7 (XY), R3C8 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R3C7 - removing <1> from <1459> leaving <459>
Squares R2C5 (XY), R3C6 (XZ) and R8C5 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R1C5 - removing <4> from <24> leaving <2>
R7C6 - removing <4> from <45> leaving <5>
R1C3 can only be <8>
R3C6 can only be <4>
R1C7 can only be <4>
R9C3 can only be <1>
R3C1 can only be <7>
R3C8 can only be <1>
R7C1 can only be <8>
R2C3 can only be <9>
R3C4 can only be <5>
R5C8 can only be <4>
R7C9 can only be <1>
R7C3 can only be <4>
R5C9 can only be <5>
R9C7 can only be <8>
R2C8 can only be <5>
R3C3 can only be <2>
R2C5 can only be <7>
R8C8 can only be <9>
R3C7 can only be <9>
R3C9 can only be <8>
R4C4 can only be <4>
R5C4 can only be <2>
R8C7 can only be <5>
R7C4 can only be <7>
R5C5 can only be <1>
R4C7 can only be <1>
R8C3 can only be <7>
R8C5 can only be <4>
R4C5 can only be <5>
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