Aug 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <2>
R8C2 can only be <7>
R2C7 can only be <6>
R6C8 can only be <7>
R8C3 can only be <5>
R8C5 can only be <2>
R9C4 can only be <7>
R7C4 can only be <3>
R2C5 can only be <7>
R7C2 is the only square in row 7 that can be <6>
R7C9 is the only square in row 7 that can be <7>
R5C1 is the only square in column 1 that can be <9>
R5C3 is the only square in row 5 that can be <7>
R1C1 is the only square in row 1 that can be <7>
R5C2 is the only square in row 5 that can be <1>
Squares R9C1 and R9C3 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <8> from <458> leaving <45>
R9C7 - removing <1> from <12459> leaving <2459>
R9C8 - removing <1> from <149> leaving <49>
Intersection of row 5 with block 6. The values <345> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C7 - removing <4> from <2489> leaving <289>
Intersection of block 5 with row 5. The values <268> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain these values.
R5C7 - removing <28> from <2458> leaving <45>
R5C9 - removing <2> from <235> leaving <35>
Squares R3C1<168>, R3C2<28>, R3C3<1268> and R3C4<26> in row 3 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1268>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C5 - removing <6> from <569> leaving <59>
R3C6 - removing <2> from <235> leaving <35>
R3C8 - removing <1> from <139> leaving <39>
R7C8 is the only square in column 8 that can be <1>
R1C7 is the only square in column 7 that can be <1>
Squares R5C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C7 - removing <45> from <2459> leaving <29>
Squares R9C1, R9C3, R3C1 and R3C3 form a Type-3 Unique Rectangle on <18>. Upon close inspection, it is clear that:
(R3C1 or R3C3)<26>, R1C3<246> and R1C2<24> form a naked triplet on <246> in block 1. No other squares in the block can contain these possibilities
R3C2 - removing <2> from <28> leaving <8>
Squares R1C2, R4C2, R1C3 and R4C3 form a Type-4 Unique Rectangle on <24>.
R1C3 - removing <2> from <246> leaving <46>
R4C3 - removing <2> from <248> leaving <48>
Squares R4C3 (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>.
R6C3 - removing <6> from <268> leaving <28>
R3C1 - removing <6> from <16> leaving <1>
R9C1 can only be <8>
R9C3 can only be <1>
R6C1 can only be <6>
Squares R9C5 (XY), R9C8 (XZ) and R3C5 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R3C8 - removing <9> from <39> leaving <3>
R3C6 can only be <5>
R5C8 can only be <4>
R1C9 can only be <9>
R5C7 can only be <5>
R9C8 can only be <9>
R9C7 can only be <2>
R1C5 can only be <6>
R4C9 can only be <2>
R3C5 can only be <9>
R7C6 can only be <8>
R4C2 can only be <4>
R9C9 can only be <5>
R6C7 can only be <8>
R5C9 can only be <3>
R7C7 can only be <4>
R6C3 can only be <2>
R4C7 can only be <9>
R5C6 can only be <2>
R7C5 can only be <5>
R9C5 can only be <4>
R1C3 can only be <4>
R5C5 can only be <8>
R3C4 can only be <2>
R3C3 can only be <6>
R5C4 can only be <6>
R1C6 can only be <3>
R4C3 can only be <8>
R1C2 can only be <2>
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