Dec 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <1>
R2C6 is the only square in row 2 that can be <8>
R4C9 is the only square in row 4 that can be <3>
R2C7 is the only square in row 2 that can be <3>
R3C4 is the only square in row 3 that can be <3>
R3C6 is the only square in row 3 that can be <5>
R4C3 is the only square in row 4 that can be <6>
R6C1 can only be <7>
R2C1 can only be <6>
R4C2 can only be <4>
R4C4 can only be <7>
R5C2 is the only square in row 5 that can be <8>
R7C1 is the only square in row 7 that can be <3>
R8C5 is the only square in row 8 that can be <1>
R8C4 is the only square in row 8 that can be <8>
R8C1 is the only square in column 1 that can be <5>
Intersection of row 7 with block 9. The value <7> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <7> from <567> leaving <56>
Intersection of row 8 with block 9. The value <4> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 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 <4> from <45679> leaving <5679>
R7C8 - removing <4> from <4567> leaving <567>
R7C9 - removing <4> from <24679> leaving <2679>
Intersection of column 8 with block 6. The value <4> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C7 - removing <4> from <4579> leaving <579>
R5C9 - removing <4> from <479> leaving <79>
R6C7 - removing <4> from <469> leaving <69>
Squares R3C5 and R7C5 in column 5 and R3C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C6 - removing <6> from <2469> leaving <249>
R7C7 - removing <6> from <5679> leaving <579>
R7C8 - removing <6> from <567> leaving <57>
Squares R5C1, R5C3, R3C1 and R3C3 form a Type-1 Unique Rectangle on <12>.
R3C3 - removing <12> from <1247> leaving <47>
R3C1 is the only square in row 3 that can be <1>
R5C1 can only be <2>
R5C3 can only be <1>
R3C2 is the only square in row 3 that can be <2>
Squares R1C2 (XY), R3C3 (XZ) and R1C4 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C5 - removing <4> from <467> leaving <67>
Squares R5C9 (XY), R2C9 (XZ) and R5C5 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R2C5 - removing <4> from <479> leaving <79>
Intersection of block 2 with row 1. The value <4> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C7 - removing <4> from <467> leaving <67>
R8C7 is the only square in column 7 that can be <4>
Squares R6C7 (XY), R1C7 (XZ) and R5C9 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R5C7 - removing <7> from <579> leaving <59>
R2C9 - removing <7> from <47> leaving <4>
R3C9 - removing <7> from <467> leaving <46>
R3C9 can only be <6>
R3C5 can only be <7>
R1C7 can only be <7>
R1C2 can only be <9>
R3C3 can only be <4>
R2C5 can only be <9>
R1C4 can only be <4>
R9C2 can only be <7>
R2C3 can only be <7>
R1C6 can only be <6>
R5C5 can only be <4>
R7C5 can only be <6>
R6C6 can only be <9>
R6C7 can only be <6>
R9C6 can only be <2>
R6C8 can only be <4>
R9C3 can only be <9>
R7C6 can only be <4>
R9C4 can only be <5>
R8C3 can only be <2>
R9C8 can only be <6>
R7C4 can only be <9>
R7C7 can only be <5>
R7C8 can only be <7>
R5C7 can only be <9>
R7C9 can only be <2>
R5C8 can only be <5>
R8C9 can only be <9>
R5C9 can only be <7>
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