Aug 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <6>
R3C8 is the only square in row 3 that can be <5>
R4C6 is the only square in row 4 that can be <4>
R6C4 is the only square in row 6 that can be <2>
R6C6 is the only square in row 6 that can be <5>
R9C3 is the only square in row 9 that can be <5>
R7C2 is the only square in column 2 that can be <6>
Intersection of column 2 with block 1. The value <3> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <3> from <234> leaving <24>
R1C3 - removing <3> from <348> leaving <48>
R2C3 - removing <3> from <379> leaving <79>
R3C1 - removing <3> from <1347> leaving <147>
R3C3 - removing <3> from <134789> leaving <14789>
Squares R2C2 and R2C7 in row 2 and R8C2 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 7 can be removed.
R1C7 - removing <2> from <2346> leaving <346>
R7C7 - removing <2> from <123789> leaving <13789>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <7> from <14789> leaving <1489>
R3C7 - removing <7> from <34679> leaving <3469>
R7C3 - removing <7> from <1347> leaving <134>
R7C7 - removing <7> from <13789> leaving <1389>
R9C7 - removing <7> from <1378> leaving <138>
Squares R1C7<346>, R3C7<3469>, R4C7<169>, R6C7<16>, R7C7<1389> and R9C7<138> in column 7 form a comprehensive naked set. These 6 squares can only contain the 6 possibilities <134689>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <39> from <2379> leaving <27>
R8C7 - removing <1> from <127> leaving <27>
Intersection of row 8 with block 7. The value <1> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <1> from <12347> leaving <2347>
R7C3 - removing <1> from <134> leaving <34>
R9C1 - removing <1> from <137> leaving <37>
Squares R9C1 (XY), R5C1 (XZ) and R9C9 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R5C9 - removing <1> from <169> leaving <69>
Intersection of column 9 with block 9. The value <1> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. 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 <1> from <1389> leaving <389>
R9C7 - removing <1> from <138> leaving <38>
Squares R7C7<389>, R7C8<39> and R9C7<38> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <389>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <9> from <1279> leaving <127>
Squares R9C1 (XY), R5C1 (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>.
R4C3 - removing <1> from <16> leaving <6>
R6C3 - removing <1> from <136> leaving <36>
R6C3 can only be <3>
R7C3 can only be <4>
R5C1 can only be <1>
R1C3 can only be <8>
Squares R5C5 (XYZ), R5C6 (XZ) and R1C5 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R6C5 - removing <6> from <16> leaving <1>
R6C7 can only be <6>
R4C5 can only be <8>
R5C9 can only be <9>
R4C4 can only be <9>
R9C5 can only be <7>
R5C4 can only be <3>
R4C7 can only be <1>
R9C1 can only be <3>
R9C9 can only be <1>
R7C6 can only be <8>
R5C5 can only be <6>
R3C4 can only be <8>
R5C6 can only be <7>
R1C5 can only be <3>
R7C4 can only be <1>
R3C6 can only be <6>
R9C7 can only be <8>
R1C7 can only be <4>
R1C1 can only be <2>
R3C9 can only be <7>
R3C1 can only be <4>
R7C9 can only be <2>
R2C7 can only be <2>
R7C1 can only be <7>
R1C9 can only be <6>
R8C7 can only be <7>
R8C3 can only be <1>
R2C2 can only be <3>
R2C8 can only be <9>
R3C2 can only be <1>
R2C3 can only be <7>
R7C8 can only be <3>
R3C7 can only be <3>
R3C3 can only be <9>
R8C2 can only be <2>
R7C7 can only be <9>
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