May 08 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <7>
R2C6 can only be <1>
R3C3 is the only square in row 3 that can be <7>
R5C7 is the only square in row 5 that can be <7>
R7C7 is the only square in row 7 that can be <3>
R7C5 is the only square in row 7 that can be <7>
R7C6 is the only square in row 7 that can be <6>
R9C5 is the only square in column 5 that can be <1>
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.
R4C3 - removing <8> from <34689> leaving <3469>
Squares R2C3 and R2C7 in row 2 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C7 - removing <5> from <15689> leaving <1689>
R5C3 - removing <5> from <3589> leaving <389>
R6C3 - removing <5> from <4569> leaving <469>
R6C7 - removing <5> from <2459> leaving <249>
R7C3 - removing <5> from <12589> leaving <1289>
Squares R1C3 and R1C5 in row 1, R6C5 and R6C7 in row 6 and R9C3 and R9C7 in row 9 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
R3C5 - removing <2> from <239> leaving <39>
R7C3 - removing <2> from <1289> leaving <189>
R8C3 - removing <2> from <289> leaving <89>
R8C7 - removing <2> from <249> leaving <49>
Intersection of row 8 with block 8. The value <2> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <2> from <248> leaving <48>
Squares R1C3 (XY), R3C1 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R2C3 - removing <5> from <56> leaving <6>
R7C1 - removing <5> from <158> leaving <18>
R2C7 can only be <5>
R9C7 can only be <2>
R3C9 can only be <9>
R3C5 can only be <3>
R3C8 can only be <8>
R1C7 can only be <1>
R9C3 can only be <5>
R7C9 can only be <5>
R1C3 can only be <2>
R3C7 can only be <6>
R5C9 can only be <2>
R1C5 can only be <9>
R3C2 can only be <5>
R4C5 can only be <6>
R3C1 can only be <1>
R4C2 can only be <9>
R6C5 can only be <2>
R5C4 can only be <9>
R5C6 can only be <3>
R7C1 can only be <8>
R4C8 can only be <4>
R6C2 can only be <6>
R7C2 can only be <2>
R6C3 can only be <4>
R4C3 can only be <3>
R4C7 can only be <8>
R7C8 can only be <9>
R6C7 can only be <9>
R5C3 can only be <8>
R6C8 can only be <5>
R8C7 can only be <4>
R7C4 can only be <4>
R5C1 can only be <5>
R8C3 can only be <9>
R3C4 can only be <2>
R8C6 can only be <2>
R7C3 can only be <1>
R8C4 can only be <8>
R3C6 can only be <4>
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