Mar 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <2>
R1C4 is the only square in row 1 that can be <1>
R2C2 is the only square in row 2 that can be <9>
R5C4 is the only square in row 5 that can be <9>
R8C8 is the only square in row 8 that can be <9>
R3C4 is the only square in column 4 that can be <3>
R3C6 is the only square in row 3 that can be <7>
R2C4 can only be <2>
R8C4 can only be <4>
R7C4 can only be <7>
R2C8 is the only square in row 2 that can be <7>
R2C9 is the only square in row 2 that can be <8>
R3C9 can only be <6>
R1C9 can only be <4>
R1C2 can only be <3>
R1C1 can only be <6>
R2C3 is the only square in row 2 that can be <4>
R7C1 is the only square in row 7 that can be <4>
R8C1 is the only square in row 8 that can be <3>
R9C1 is the only square in row 9 that can be <7>
R4C3 is the only square in column 3 that can be <3>
R5C6 is the only square in column 6 that can be <4>
R9C8 is the only square in column 8 that can be <6>
R9C9 is the only square in row 9 that can be <3>
R5C8 is the only square in row 5 that can be <3>
Intersection of row 5 with block 4. The value <8> 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 <8> from <28> leaving <2>
R6C2 - removing <8> from <2478> leaving <247>
Intersection of column 6 with block 8. The values <12> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C5 - removing <12> from <1256> leaving <56>
Intersection of column 7 with block 9. The value <5> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. 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 <125> leaving <12>
Intersection of block 9 with row 7. The values <28> only appears in one or more of squares R7C7, R7C8 and R7C9 of block 9. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C6 - removing <2> from <125> leaving <15>
Squares R2C5, R2C6, R8C5 and R8C6 form a Type-1 Unique Rectangle on <56>.
R8C6 - removing <56> from <1256> leaving <12>
R8C5 is the only square in row 8 that can be <6>
R2C5 can only be <5>
R2C6 can only be <6>
Squares R3C1, R5C1, R3C2 and R5C2 form a Type-4 Unique Rectangle on <58>.
R3C2 - removing <5> from <258> leaving <28>
R5C2 - removing <5> from <578> leaving <78>
Squares R4C8 (XY), R5C9 (XZ) and R4C2 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R4C9 - removing <5> from <125> leaving <12>
R5C1 - removing <5> from <58> leaving <8>
R5C2 can only be <7>
R3C1 can only be <5>
R5C5 can only be <2>
R6C2 can only be <4>
R5C9 can only be <5>
R4C5 can only be <1>
R6C8 can only be <8>
R4C2 can only be <5>
R6C7 can only be <1>
R7C8 can only be <2>
R7C9 can only be <1>
R4C8 can only be <4>
R7C6 can only be <5>
R4C9 can only be <2>
R8C7 can only be <5>
R8C2 can only be <2>
R7C7 can only be <8>
R3C3 can only be <2>
R3C2 can only be <8>
R9C3 can only be <5>
R6C5 can only be <7>
R9C6 can only be <2>
R8C6 can only be <1>
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