Oct 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 is the only square in row 4 that can be <1>
R6C7 is the only square in row 6 that can be <9>
R8C3 is the only square in column 3 that can be <1>
R7C4 is the only square in column 4 that can be <8>
R7C6 is the only square in row 7 that can be <9>
R3C6 is the only square in column 6 that can be <1>
R7C9 is the only square in column 9 that can be <6>
R7C8 can only be <7>
R7C1 can only be <5>
R8C1 can only be <8>
R9C1 can only be <7>
R7C7 is the only square in row 7 that can be <1>
R1C9 is the only square in row 1 that can be <1>
R8C2 is the only square in column 2 that can be <6>
R5C8 is the only square in column 8 that can be <6>
R6C9 is the only square in column 9 that can be <2>
R6C4 can only be <3>
R6C6 can only be <7>
R5C7 can only be <8>
R6C2 can only be <8>
R4C1 is the only square in row 4 that can be <3>
R3C1 can only be <9>
R1C4 is the only square in row 1 that can be <9>
R2C8 is the only square in row 2 that can be <9>
R4C3 is the only square in row 4 that can be <9>
R9C8 is the only square in row 9 that can be <8>
R3C8 can only be <3>
R1C2 is the only square in row 1 that can be <3>
Squares R5C2 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <2> from <245> leaving <45>
R5C6 - removing <2> from <245> leaving <45>
Squares R8C7, R9C7, R8C5 and R9C5 form a Type-4 Unique Rectangle on <23>.
R8C5 - removing <2> from <235> leaving <35>
R9C5 - removing <2> from <2346> leaving <346>
Squares R2C9, R3C9, R2C3 and R3C3 form a Type-4 Unique Rectangle on <48>.
R2C3 - removing <4> from <4578> leaving <578>
R3C3 - removing <4> from <4578> leaving <578>
Squares R8C6 (XY), R7C5 (XZ) and R5C6 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R9C6 - removing <4> from <246> leaving <26>
R5C6 is the only square in column 6 that can be <4>
R5C4 can only be <5>
R8C6 is the only square in column 6 that can be <5>
R8C5 can only be <3>
R8C7 can only be <2>
R9C7 can only be <3>
Intersection of column 4 with block 2. The value <4> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <4> from <457> leaving <57>
R2C5 - removing <4> from <4567> leaving <567>
R3C5 - removing <4> from <2457> leaving <257>
R1C3 is the only square in row 1 that can be <4>
R9C3 can only be <2>
R3C2 can only be <7>
R5C2 can only be <2>
R5C3 can only be <7>
R7C2 can only be <4>
R7C5 can only be <2>
R3C5 can only be <5>
R9C6 can only be <6>
R9C5 can only be <4>
R4C6 can only be <2>
R3C3 can only be <8>
R1C5 can only be <7>
R4C4 can only be <6>
R1C7 can only be <5>
R2C5 can only be <6>
R2C7 can only be <7>
R2C4 can only be <4>
R3C9 can only be <4>
R2C3 can only be <5>
R3C4 can only be <2>
R2C9 can only be <8>
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