Mar 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C5 can only be <4>
R4C4 can only be <4>
R5C5 can only be <8>
R6C6 can only be <5>
R7C5 can only be <3>
R1C4 can only be <9>
R6C4 can only be <7>
R6C1 can only be <1>
R6C9 can only be <4>
R4C6 can only be <3>
R9C6 can only be <9>
R9C4 can only be <1>
R1C6 can only be <2>
R1C1 is the only square in row 1 that can be <8>
R1C9 is the only square in row 1 that can be <6>
R9C7 is the only square in row 9 that can be <8>
R7C2 is the only square in row 7 that can be <8>
R9C3 is the only square in row 9 that can be <7>
R7C7 is the only square in row 7 that can be <7>
Squares R2C2 and R2C8 in row 2 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.
R2C3 - removing <59> from <2459> leaving <24>
R2C7 - removing <59> from <2459> leaving <24>
Intersection of column 2 with block 1. The value <5> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <5> from <3569> leaving <369>
R3C3 - removing <5> from <2359> leaving <239>
Squares R1C3 and R1C7 in row 1 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <3> from <239> leaving <29>
R3C7 - removing <3> from <2359> leaving <259>
Squares R4C1 and R4C9 in row 4 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C9 - removing <5> from <1359> leaving <139>
R7C1 - removing <5> from <569> leaving <69>
R7C9 - removing <5> from <159> leaving <19>
Squares R7C1 and R8C2 in block 7 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.
R7C3 - removing <9> from <159> leaving <15>
R8C3 - removing <9> from <139> leaving <13>
Squares R8C7 (XY), R8C3 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R7C3 - removing <1> from <15> leaving <5>
R8C8 - removing <1> from <169> leaving <69>
R5C3 can only be <9>
R9C1 can only be <3>
R9C9 can only be <5>
R8C3 can only be <1>
R4C9 can only be <9>
R4C1 can only be <5>
R7C9 can only be <1>
R5C7 can only be <5>
R3C3 can only be <2>
R3C9 can only be <3>
R3C7 can only be <9>
R2C3 can only be <4>
R3C1 can only be <6>
R8C7 can only be <3>
R2C8 can only be <5>
R1C7 can only be <4>
R1C3 can only be <3>
R2C7 can only be <2>
R2C2 can only be <9>
R3C8 can only be <1>
R3C2 can only be <5>
R7C1 can only be <9>
R7C8 can only be <6>
R8C2 can only be <6>
R8C8 can only be <9>
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