Feb 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <4>
R1C6 can only be <9>
R1C3 can only be <8>
R1C7 is the only square in row 1 that can be <5>
R2C5 is the only square in row 2 that can be <2>
R3C5 can only be <3>
R3C9 is the only square in row 3 that can be <2>
R5C6 is the only square in row 5 that can be <6>
R6C5 is the only square in row 6 that can be <4>
R6C6 is the only square in row 6 that can be <5>
R9C6 can only be <2>
R4C6 can only be <8>
R4C4 is the only square in row 4 that can be <2>
R8C3 is the only square in row 8 that can be <2>
R9C3 is the only square in row 9 that can be <5>
R3C1 is the only square in column 1 that can be <4>
Squares R4C1 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C2 - removing <39> from <3789> leaving <78>
R6C1 - removing <3> from <378> leaving <78>
Intersection of column 9 with block 9. The value <9> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <9> from <1589> leaving <158>
Squares R5C2 and R5C8 in row 5 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R7C2 - removing <8> from <1389> leaving <139>
R7C8 - removing <8> from <158> leaving <15>
Squares R7C5 and R7C8 in row 7 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 row.
R7C1 - removing <1> from <1389> leaving <389>
R7C2 - removing <1> from <139> leaving <39>
R7C9 - removing <1> from <1389> leaving <389>
Squares R7C5, R7C8, R8C5 and R8C8 form a Type-4 Unique Rectangle on <15>.
R8C5 - removing <1> from <157> leaving <57>
R8C8 - removing <1> from <158> leaving <58>
Squares R8C5 (XY), R7C5 (XZ) and R8C7 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R7C8 - removing <1> from <15> leaving <5>
R7C5 can only be <1>
R8C8 can only be <8>
R8C2 can only be <1>
R4C5 can only be <9>
R9C4 can only be <7>
R8C7 can only be <7>
R3C2 can only be <9>
R8C5 can only be <5>
R2C7 can only be <4>
R6C4 can only be <3>
R2C8 can only be <9>
R2C3 can only be <3>
R3C8 can only be <1>
R7C2 can only be <3>
R5C8 can only be <4>
R1C9 can only be <7>
R4C1 can only be <3>
R5C5 can only be <7>
R5C2 can only be <8>
R6C9 can only be <8>
R5C4 can only be <1>
R6C1 can only be <7>
R7C9 can only be <9>
R2C2 can only be <7>
R9C1 can only be <9>
R7C1 can only be <8>
R1C1 can only be <1>
R5C3 can only be <9>
R4C9 can only be <1>
R9C9 can only be <3>
R5C7 can only be <3>
R9C7 can only be <1>
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