Jan 04 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <7>
R2C4 is the only square in row 2 that can be <2>
R3C5 can only be <1>
R5C5 can only be <7>
R2C7 is the only square in row 2 that can be <4>
R3C1 is the only square in row 3 that can be <2>
R4C9 is the only square in row 4 that can be <2>
R4C1 is the only square in row 4 that can be <4>
R5C9 is the only square in row 5 that can be <4>
R7C5 is the only square in row 7 that can be <2>
R8C7 is the only square in row 8 that can be <2>
R8C6 is the only square in row 8 that can be <4>
R9C4 is the only square in row 9 that can be <7>
R8C4 can only be <8>
R1C4 can only be <9>
R9C5 can only be <3>
R9C6 can only be <6>
R1C5 can only be <8>
R4C6 can only be <9>
R6C6 can only be <8>
R2C8 is the only square in row 2 that can be <8>
Intersection of row 2 with block 1. The value <9> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <9> from <569> leaving <56>
Intersection of row 5 with block 4. The value <9> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <9> from <1569> leaving <156>
R6C2 - removing <9> from <13569> leaving <1356>
R2C2 is the only square in column 2 that can be <9>
Intersection of row 8 with block 7. The value <5> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <5> from <1589> leaving <189>
R9C3 - removing <5> from <159> leaving <19>
Squares R1C3 and R5C3 in column 3 and R1C7 and R5C7 in column 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 5 can be removed.
R1C1 - removing <6> from <156> leaving <15>
R5C1 - removing <6> from <169> leaving <19>
Squares R1C1 and R1C3 in row 1, R5C1, R5C3 and R5C7 in row 5 and R9C1, R9C3 and R9C7 in row 9 form a Swordfish pattern on possibility <1>. All other instances of this possibility in columns 1, 3 and 7 can be removed.
R6C1 - removing <1> from <156> leaving <56>
R8C3 - removing <1> from <15> leaving <5>
R2C3 can only be <3>
R2C6 can only be <5>
R1C6 can only be <3>
Squares R1C1 (XY), R1C3 (XZ) and R6C1 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R5C3 - removing <6> from <169> leaving <19>
R5C7 is the only square in row 5 that can be <6>
R1C7 can only be <5>
R1C1 can only be <1>
R9C7 can only be <1>
R3C9 can only be <9>
R3C8 can only be <6>
R6C9 can only be <3>
R7C9 can only be <8>
R4C8 can only be <1>
R7C1 can only be <6>
R9C9 can only be <5>
R9C3 can only be <9>
R8C8 can only be <7>
R1C3 can only be <6>
R5C1 can only be <9>
R3C2 can only be <5>
R4C4 can only be <6>
R6C8 can only be <9>
R5C3 can only be <1>
R9C1 can only be <8>
R6C2 can only be <6>
R6C1 can only be <5>
R6C4 can only be <1>
R4C2 can only be <3>
R7C2 can only be <7>
R7C8 can only be <3>
R8C2 can only be <1>
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