Nov 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 is the only square in row 2 that can be <6>
R3C5 is the only square in row 3 that can be <5>
R3C7 is the only square in row 3 that can be <6>
R3C9 is the only square in row 3 that can be <3>
R4C6 is the only square in row 4 that can be <6>
R4C3 is the only square in row 4 that can be <2>
R6C6 is the only square in row 6 that can be <2>
R6C3 is the only square in row 6 that can be <5>
R7C1 is the only square in row 7 that can be <2>
R9C3 is the only square in row 9 that can be <6>
R5C3 is the only square in column 3 that can be <1>
Squares R6C2 and R6C4 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C7 - removing <89> from <1489> leaving <14>
Intersection of row 2 with block 2. The value <9> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <9> from <489> leaving <48>
Intersection of row 9 with block 9. The value <7> 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.
R7C7 - removing <7> from <13478> leaving <1348>
R7C9 - removing <7> from <1478> leaving <148>
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 <1348> leaving <348>
Squares R2C4 and R2C9 in row 2 and R8C4 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 4 and 9 can be removed.
R3C4 - removing <4> from <1478> leaving <178>
R7C4 - removing <4> from <134789> leaving <13789>
R7C9 - removing <4> from <148> leaving <18>
R3C3 is the only square in row 3 that can be <4>
R9C2 is the only square in column 2 that can be <4>
Squares R4C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <7> from <147> leaving <14>
Squares R1C2 and R1C7 in row 1, R4C2, R4C7 and R4C8 in row 4 and R9C7 and R9C8 in row 9 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 2, 7 and 8 can be removed.
R5C7 - removing <7> from <3789> leaving <389>
Squares R6C2, R6C4, R4C2 and R4C4 form a Type-3 Unique Rectangle on <89>. Upon close inspection, it is clear that:
(R4C2 or R4C4)<37> and R4C8<37> form a naked pair on <37> in row 4. No other squares in the row can contain these possibilities
R4C7 - removing <37> from <3789> leaving <89>
Squares R6C7, R6C8, R1C7 and R1C8 form a Type-1 Unique Rectangle on <14>.
R1C7 - removing <14> from <147> leaving <7>
R2C9 can only be <4>
R1C8 can only be <1>
R6C8 can only be <4>
R6C7 can only be <1>
R1C5 is the only square in row 1 that can be <4>
R7C7 is the only square in row 7 that can be <4>
R8C4 is the only square in row 8 that can be <4>
R9C8 is the only square in row 9 that can be <7>
R4C8 can only be <3>
R4C2 is the only square in row 4 that can be <7>
R5C5 is the only square in row 5 that can be <3>
R9C5 can only be <8>
R9C7 can only be <3>
R7C5 can only be <9>
R7C3 can only be <8>
R8C6 can only be <1>
R8C9 can only be <8>
R7C6 can only be <7>
R8C1 can only be <9>
R5C9 can only be <7>
R7C9 can only be <1>
R1C3 can only be <9>
R7C4 can only be <3>
R2C6 can only be <9>
R3C6 can only be <8>
R5C1 can only be <8>
R1C2 can only be <8>
R2C4 can only be <7>
R3C1 can only be <7>
R5C7 can only be <9>
R6C2 can only be <9>
R4C7 can only be <8>
R6C4 can only be <8>
R4C4 can only be <9>
R3C4 can only be <1>
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