Sep 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 is the only square in row 4 that can be <6>
R6C6 is the only square in row 6 that can be <3>
R3C1 is the only square in column 1 that can be <1>
R5C5 is the only square in column 5 that can be <5>
R8C6 is the only square in column 6 that can be <5>
R7C9 is the only square in column 9 that can be <1>
R1C7 is the only square in column 7 that can be <1>
Squares R4C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <7> from <247> leaving <24>
Intersection of block 2 with row 2. The value <7> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.
R2C1 - removing <7> from <2479> leaving <249>
R2C3 - removing <7> from <2679> leaving <269>
R2C9 - removing <7> from <4789> leaving <489>
Intersection of block 4 with column 2. The value <9> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain this value.
R3C2 - removing <9> from <24579> leaving <2457>
R9C2 - removing <9> from <2789> leaving <278>
Squares R2C4<27>, R5C4<278> and R8C4<78> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <278>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C4 - removing <78> from <1789> leaving <19>
R6C4 - removing <2> from <129> leaving <19>
Squares R2C1 and R5C1 in column 1 and R2C4 and R5C4 in column 4 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C3 - removing <2> from <269> leaving <69>
R2C7 - removing <2> from <2468> leaving <468>
R3C7 is the only square in column 7 that can be <2>
Squares R2C7 and R2C9 in row 2, R5C4 and R5C9 in row 5 and R8C4, R8C7 and R8C9 in row 8 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 4, 7 and 9 can be removed.
R7C7 - removing <8> from <468> leaving <46>
R9C7 - removing <8> from <38> leaving <3>
R8C3 is the only square in row 8 that can be <3>
Squares R5C6 (XY), R5C9 (XZ) and R4C5 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R4C8 - removing <8> from <18> leaving <1>
R5C4 - removing <8> from <278> leaving <27>
R4C4 can only be <9>
R6C8 can only be <4>
R6C5 can only be <2>
R5C9 can only be <8>
R4C2 can only be <7>
R6C4 can only be <1>
R6C2 can only be <9>
R1C5 can only be <4>
R5C4 can only be <7>
R2C6 can only be <7>
R2C4 can only be <2>
R5C6 can only be <4>
R4C5 can only be <8>
R1C2 can only be <2>
R5C1 can only be <2>
R9C5 can only be <7>
R8C4 can only be <8>
R8C7 can only be <4>
R7C7 can only be <6>
R9C2 can only be <8>
R2C7 can only be <8>
R9C8 can only be <9>
R9C3 can only be <2>
R3C8 can only be <7>
R8C9 can only be <7>
R1C8 can only be <6>
R7C8 can only be <8>
R8C1 can only be <9>
R1C3 can only be <7>
R2C1 can only be <4>
R7C3 can only be <5>
R2C9 can only be <9>
R7C1 can only be <7>
R3C2 can only be <5>
R2C3 can only be <6>
R3C9 can only be <4>
R3C3 can only be <9>
R7C2 can only be <4>
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