Oct 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 can only be <1>
R3C7 can only be <7>
R1C1 is the only square in row 1 that can be <2>
R4C6 is the only square in row 4 that can be <2>
R9C8 is the only square in row 9 that can be <2>
R5C1 is the only square in column 1 that can be <1>
R2C9 is the only square in column 9 that can be <1>
Squares R4C2 and R6C2 in column 2 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.
R1C2 - removing <3> from <34689> leaving <4689>
R2C2 - removing <3> from <34689> leaving <4689>
R8C2 - removing <37> from <36789> leaving <689>
R9C2 - removing <37> from <34679> leaving <469>
R2C1 is the only square in row 2 that can be <3>
Intersection of block 2 with row 2. The value <4> 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.
R2C2 - removing <4> from <4689> leaving <689>
Intersection of block 8 with row 8. The value <5> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C1 - removing <5> from <578> leaving <78>
R8C8 - removing <5> from <5678> leaving <678>
R1C8 is the only square in column 8 that can be <5>
Squares R1C3 and R9C3 in column 3 and R1C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C2 - removing <6> from <4689> leaving <489>
R9C2 - removing <6> from <469> leaving <49>
R1C9 - removing <6> from <3468> leaving <348>
R9C9 - removing <6> from <3679> leaving <379>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C9 - removing <8> from <348> leaving <34>
R8C1 - removing <8> from <78> leaving <7>
R8C9 - removing <8> from <36789> leaving <3679>
R9C9 is the only square in row 9 that can be <7>
R5C9 can only be <6>
R5C6 can only be <5>
R5C4 can only be <8>
R8C6 can only be <9>
R8C9 can only be <3>
R2C6 can only be <4>
R9C5 can only be <3>
R8C4 can only be <5>
R1C9 can only be <4>
R7C7 can only be <5>
R3C9 can only be <8>
R6C6 can only be <6>
R3C1 can only be <4>
R7C9 can only be <9>
R2C8 can only be <6>
R5C5 can only be <7>
R2C4 can only be <9>
R6C5 can only be <1>
R6C8 can only be <7>
R4C5 can only be <9>
R6C2 can only be <3>
R4C8 can only be <1>
R7C1 can only be <8>
R9C7 can only be <6>
R7C3 can only be <3>
R9C3 can only be <9>
R1C7 can only be <3>
R8C8 can only be <8>
R4C4 can only be <3>
R1C5 can only be <8>
R2C2 can only be <8>
R9C1 can only be <5>
R4C2 can only be <7>
R6C4 can only be <4>
R8C2 can only be <6>
R9C2 can only be <4>
R1C3 can only be <6>
R1C2 can only be <9>
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