Jul 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 can only be <6>
R3C5 can only be <5>
R7C5 can only be <6>
R9C3 can only be <4>
R2C3 can only be <1>
R8C3 can only be <9>
R5C3 can only be <3>
R5C8 can only be <7>
R2C1 is the only square in row 2 that can be <4>
R2C9 is the only square in row 2 that can be <5>
R2C8 is the only square in row 2 that can be <2>
R8C8 can only be <3>
R4C5 is the only square in row 4 that can be <7>
R5C6 is the only square in row 5 that can be <2>
R5C4 is the only square in row 5 that can be <5>
R5C9 is the only square in row 5 that can be <4>
R8C9 is the only square in row 8 that can be <2>
R8C1 is the only square in row 8 that can be <5>
Intersection of row 1 with block 3. The value <3> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <3> from <378> leaving <78>
R1C7 is the only square in column 7 that can be <3>
Intersection of row 5 with block 4. The value <6> 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.
R6C1 - removing <6> from <168> leaving <18>
Intersection of row 9 with block 9. The value <1> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <1> from <167> leaving <67>
Squares R6C1<18>, R6C5<138> and R6C9<138> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <138>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <13> from <1346> leaving <46>
R6C6 - removing <8> from <468> leaving <46>
Squares R2C2 and R2C7 in row 2 and R8C2 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 7 can be removed.
R9C7 - removing <7> from <167> leaving <16>
Squares R2C2 and R5C2 in column 2 and R2C7 and R5C7 in column 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 5 can be removed.
R5C1 - removing <8> from <1689> leaving <169>
R5C5 - removing <8> from <189> leaving <19>
Squares R5C5 (XY), R5C7 (XZ) and R4C6 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R4C9 - removing <8> from <138> leaving <13>
Squares R4C4 and R4C9 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <1> from <189> leaving <89>
Squares R5C5 (XY), R8C5 (XZ) and R4C6 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R8C6 - removing <8> from <48> leaving <4>
R6C5 - removing <8> from <138> leaving <13>
R8C4 can only be <1>
R6C6 can only be <6>
R6C4 can only be <4>
R2C6 can only be <9>
R8C5 can only be <8>
R4C4 can only be <3>
R2C5 can only be <3>
R4C6 can only be <8>
R4C9 can only be <1>
R2C4 can only be <6>
R6C5 can only be <1>
R4C1 can only be <9>
R9C9 can only be <7>
R5C7 can only be <8>
R5C2 can only be <6>
R2C7 can only be <7>
R6C9 can only be <3>
R6C1 can only be <8>
R5C5 can only be <9>
R9C1 can only be <6>
R1C9 can only be <8>
R8C7 can only be <6>
R1C1 can only be <7>
R2C2 can only be <8>
R5C1 can only be <1>
R8C2 can only be <7>
R9C7 can only be <1>
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