Jun 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 can only be <2>
R5C5 can only be <8>
R5C6 can only be <5>
R2C8 is the only square in row 2 that can be <8>
R3C3 is the only square in row 3 that can be <2>
R3C6 is the only square in row 3 that can be <8>
R5C8 is the only square in row 5 that can be <6>
R3C7 is the only square in row 3 that can be <6>
R6C1 is the only square in row 6 that can be <5>
R7C3 is the only square in row 7 that can be <8>
R6C9 is the only square in row 6 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R7C2 is the only square in row 7 that can be <1>
R8C7 is the only square in row 8 that can be <5>
R8C8 is the only square in row 8 that can be <9>
R7C6 is the only square in row 7 that can be <9>
R9C5 is the only square in row 9 that can be <2>
R8C2 is the only square in column 2 that can be <7>
R1C4 is the only square in column 4 that can be <1>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <7> from <367> leaving <36>
Intersection of row 4 with block 6. The value <9> only appears in one or more of squares R4C7, R4C8 and R4C9 of row 4. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C9 - removing <9> from <349> leaving <34>
Intersection of column 5 with block 2. The value <3> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C4 - removing <3> from <347> leaving <47>
Squares R5C1 and R9C1 in column 1 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <4> from <349> leaving <39>
R9C4 - removing <4> from <347> leaving <37>
Intersection of column 2 with block 1. The value <4> 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.
R2C3 - removing <4> from <346> leaving <36>
Squares R2C3 and R2C5 in row 2 and R8C3 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.
R1C5 - removing <6> from <36> leaving <3>
Squares R2C3 (XY), R2C7 (XZ) and R1C1 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R1C9 - removing <9> from <79> leaving <7>
R2C2 - removing <9> from <349> leaving <34>
R1C6 can only be <6>
R3C8 can only be <3>
R3C2 can only be <4>
R7C8 can only be <7>
R2C7 can only be <9>
R1C1 can only be <9>
R9C6 can only be <7>
R2C5 can only be <4>
R2C2 can only be <3>
R8C5 can only be <6>
R3C4 can only be <7>
R9C4 can only be <3>
R8C3 can only be <4>
R9C9 can only be <4>
R7C4 can only be <4>
R9C1 can only be <6>
R5C9 can only be <3>
R7C7 can only be <3>
R5C1 can only be <4>
R2C3 can only be <6>
R5C2 can only be <9>
R6C3 can only be <1>
R4C9 can only be <9>
R4C7 can only be <7>
R6C5 can only be <7>
R4C3 can only be <3>
R6C7 can only be <4>
R4C5 can only be <1>
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