Apr 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R6C3 can only be <6>
R8C5 can only be <7>
R6C7 can only be <8>
R2C5 can only be <9>
R7C6 can only be <1>
R1C5 can only be <3>
R7C4 can only be <3>
R3C6 can only be <7>
R3C5 can only be <8>
R3C4 can only be <1>
R3C7 is the only square in row 3 that can be <4>
R3C9 is the only square in row 3 that can be <3>
R7C3 is the only square in row 7 that can be <8>
R7C5 is the only square in row 7 that can be <4>
R9C5 can only be <6>
R9C3 is the only square in row 9 that can be <4>
R3C2 is the only square in column 2 that can be <6>
R3C8 can only be <9>
R7C7 is the only square in row 7 that can be <9>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C3 - removing <1> from <179> leaving <79>
R1C7 - removing <1> from <167> leaving <67>
R9C7 - removing <1> from <157> leaving <57>
Squares R4C3, R4C7, R5C3 and R5C7 form a Type-4 Unique Rectangle on <35>.
R5C3 - removing <5> from <3579> leaving <379>
R5C7 - removing <5> from <2356> leaving <236>
Squares R7C1 (XYZ), R7C2 (XZ) and R3C1 (YZ) form an XYZ-Wing pattern on <5>. All squares that are buddies of all three squares cannot be <5>.
R9C1 - removing <5> from <157> leaving <17>
Intersection of row 9 with block 9. The value <5> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. 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 <5> from <567> leaving <67>
Squares R5C9 (XY), R5C2 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R7C2 - removing <7> from <57> leaving <5>
R5C2 can only be <7>
Intersection of column 3 with block 1. The value <7> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <7> from <179> leaving <19>
Squares R7C9 (XY), R5C9 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R9C9 - removing <5> from <157> leaving <17>
R4C7 - removing <5> from <35> leaving <3>
R4C3 can only be <5>
R3C3 can only be <2>
R5C1 can only be <9>
R5C3 can only be <3>
R1C1 can only be <1>
R9C1 can only be <7>
R2C3 can only be <7>
R2C7 can only be <1>
R1C3 can only be <9>
R8C7 can only be <2>
R3C1 can only be <5>
R8C3 can only be <1>
R5C7 can only be <6>
R7C8 can only be <6>
R9C7 can only be <5>
R9C9 can only be <1>
R7C1 can only be <2>
R5C8 can only be <2>
R5C9 can only be <5>
R1C7 can only be <7>
R7C9 can only be <7>
R1C9 can only be <6>
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