Mar 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <2>
R8C5 can only be <9>
R2C5 can only be <7>
R9C4 can only be <3>
R9C6 can only be <1>
R6C4 can only be <6>
R1C6 can only be <9>
R6C9 can only be <3>
R4C4 can only be <9>
R6C1 can only be <1>
R6C6 can only be <7>
R4C9 can only be <6>
R5C8 can only be <4>
R1C4 can only be <8>
R4C6 can only be <3>
R4C1 can only be <4>
R5C2 can only be <3>
R1C1 can only be <2>
R9C1 can only be <5>
R2C2 is the only square in row 2 that can be <4>
R3C8 is the only square in row 3 that can be <5>
R8C9 is the only square in row 8 that can be <5>
Intersection of row 3 with block 1. The value <7> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <7> from <167> leaving <16>
Intersection of column 9 with block 3. The value <1> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <1> from <139> leaving <39>
Squares R1C2<16>, R3C2<67> and R8C2<17> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <167>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C2 - removing <1> from <129> leaving <29>
R9C2 - removing <7> from <279> leaving <29>
Intersection of row 9 with block 9. The value <7> 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.
R8C8 - removing <7> from <367> leaving <36>
Squares R2C1, R8C1, R2C3 and R8C3 form a Type-4 Unique Rectangle on <38>.
R2C3 - removing <3> from <138> leaving <18>
R8C3 - removing <3> from <1378> leaving <178>
Squares R7C2, R9C2, R7C8 and R9C8 form a Type-3 Unique Rectangle on <29>. Upon close inspection, it is clear that:
(R7C8 or R9C8)<37>, R8C8<36> and R1C8<67> form a naked triplet on <367> in column 8. No other squares in the column can contain these possibilities
R2C8 - removing <3> from <239> leaving <29>
Intersection of column 8 with block 9. The value <3> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <3> from <139> leaving <19>
R8C7 - removing <3> from <136> leaving <16>
Squares R2C3 (XY), R7C3 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R8C1 - removing <3> from <38> leaving <8>
R3C3 - removing <3> from <37> leaving <7>
R3C2 can only be <6>
R8C3 can only be <1>
R2C1 can only be <3>
R8C2 can only be <7>
R8C7 can only be <6>
R2C3 can only be <8>
R7C3 can only be <3>
R8C8 can only be <3>
R3C7 can only be <3>
R2C7 can only be <9>
R2C8 can only be <2>
R7C7 can only be <1>
R2C9 can only be <1>
R7C8 can only be <9>
R1C9 can only be <7>
R1C2 can only be <1>
R7C2 can only be <2>
R9C8 can only be <7>
R9C9 can only be <2>
R1C8 can only be <6>
R9C2 can only be <9>
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