Jan 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 can only be <1>
R6C9 can only be <5>
R5C8 can only be <4>
R5C7 can only be <7>
R6C4 is the only square in column 4 that can be <4>
Squares R5C2 and R5C4 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C3 - removing <29> from <129> leaving <1>
R5C5 - removing <2> from <1235> leaving <135>
R5C6 - removing <9> from <359> leaving <35>
R6C1 can only be <8>
R6C6 can only be <6>
R6C5 can only be <1>
R1C6 can only be <3>
R1C8 can only be <1>
R5C6 can only be <5>
R5C5 can only be <3>
R9C6 can only be <9>
R9C8 can only be <5>
R4C6 can only be <8>
R2C1 is the only square in row 2 that can be <1>
R3C7 is the only square in row 3 that can be <5>
R8C5 is the only square in row 8 that can be <5>
R7C2 is the only square in row 7 that can be <5>
R7C3 is the only square in row 7 that can be <8>
R2C7 is the only square in row 2 that can be <8>
R1C2 is the only square in row 1 that can be <8>
R9C7 is the only square in row 9 that can be <1>
R9C3 is the only square in row 9 that can be <4>
R2C5 is the only square in row 2 that can be <4>
R3C1 is the only square in row 3 that can be <4>
R7C7 is the only square in row 7 that can be <4>
R8C1 is the only square in column 1 that can be <7>
Squares R5C2 and R5C4 in row 5 and R9C2 and R9C4 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 4 can be removed.
R3C2 - removing <2> from <269> leaving <69>
R4C4 - removing <2> from <279> leaving <79>
Squares R2C3 and R3C2 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C3 - removing <6> from <267> leaving <27>
R3C3 - removing <69> from <2679> leaving <27>
Squares R1C3 and R3C3 in column 3 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 column.
R8C3 - removing <2> from <269> leaving <69>
Intersection of row 8 with block 9. The value <2> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C9 - removing <2> from <2369> leaving <369>
Squares R2C3 and R2C9 in row 2 and R8C3 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 9 can be removed.
R3C9 - removing <9> from <2369> leaving <236>
R7C9 - removing <9> from <369> leaving <36>
Squares R2C9 (XY), R7C9 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R3C9 - removing <3> from <236> leaving <26>
R7C8 - removing <3> from <39> leaving <9>
R7C1 can only be <2>
R3C8 can only be <3>
R7C5 can only be <6>
R4C1 can only be <9>
R9C2 can only be <6>
R7C9 can only be <3>
R3C5 can only be <7>
R9C4 can only be <2>
R3C2 can only be <9>
R8C3 can only be <9>
R5C4 can only be <9>
R5C2 can only be <2>
R2C3 can only be <6>
R3C3 can only be <2>
R4C5 can only be <2>
R1C4 can only be <6>
R4C4 can only be <7>
R1C7 can only be <2>
R1C3 can only be <7>
R8C7 can only be <6>
R3C9 can only be <6>
R2C9 can only be <9>
R8C9 can only be <2>
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