Jul 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <5>
R5C4 can only be <7>
R5C8 is the only square in row 5 that can be <5>
R5C9 is the only square in row 5 that can be <4>
R8C8 is the only square in row 8 that can be <7>
R9C8 is the only square in column 8 that can be <4>
R9C5 is the only square in row 9 that can be <3>
R3C5 can only be <7>
R8C4 can only be <4>
R2C4 can only be <3>
R2C2 is the only square in row 2 that can be <7>
R2C5 is the only square in row 2 that can be <4>
R1C5 can only be <2>
R1C2 is the only square in row 1 that can be <4>
R2C8 is the only square in row 2 that can be <2>
R8C7 is the only square in row 8 that can be <3>
R9C2 is the only square in row 9 that can be <5>
R8C5 is the only square in row 8 that can be <5>
R6C8 is the only square in block 6 that can be <9>
Intersection of column 2 with block 7. The value <9> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <9> from <2689> leaving <268>
Intersection of block 9 with column 9. The value <8> only appears in one or more of squares R7C9, R8C9 and R9C9 of block 9. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R1C9 - removing <8> from <89> leaving <9>
R2C9 - removing <8> from <1689> leaving <169>
R2C1 is the only square in row 2 that can be <9>
Squares R4C2<168>, R5C3<168> and R6C2<18> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <168>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C1 - removing <68> from <2368> leaving <23>
R5C2 - removing <168> from <12368> leaving <23>
Intersection of column 1 with block 7. The value <6> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <6> from <169> leaving <19>
R8C2 - removing <6> from <12689> leaving <1289>
R8C3 - removing <6> from <168> leaving <18>
Squares R4C2, R4C5 and R4C8 in row 4, R6C2 and R6C5 in row 6 and R7C2 and R7C8 in row 7 form a Swordfish pattern on possibility <1>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R5C5 - removing <1> from <1689> leaving <689>
R8C2 - removing <1> from <1289> leaving <289>
Squares R3C2 and R3C8 in row 3, R4C2 and R4C5 in row 4 and R7C5 and R7C8 in row 7 form a Swordfish pattern on possibility <6>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R5C5 - removing <6> from <689> leaving <89>
Squares R2C3 (XY), R2C9 (XZ) and R8C3 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R8C9 - removing <1> from <168> leaving <68>
R8C3 is the only square in row 8 that can be <1>
R7C2 can only be <9>
R7C5 can only be <6>
R7C8 can only be <1>
R8C6 can only be <9>
R4C8 can only be <8>
R5C6 can only be <6>
R4C5 can only be <1>
R1C8 can only be <3>
R5C7 can only be <1>
R5C3 can only be <8>
R2C7 can only be <8>
R1C1 can only be <8>
R3C8 can only be <6>
R2C3 can only be <6>
R3C2 can only be <3>
R2C9 can only be <1>
R4C2 can only be <6>
R6C5 can only be <8>
R5C5 can only be <9>
R6C2 can only be <1>
R9C1 can only be <6>
R5C2 can only be <2>
R5C1 can only be <3>
R8C2 can only be <8>
R8C9 can only be <6>
R8C1 can only be <2>
R9C9 can only be <8>
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