May 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <6>
R9C4 can only be <5>
R9C6 can only be <4>
R5C6 can only be <5>
R8C5 can only be <1>
R1C6 can only be <8>
R7C5 can only be <8>
R9C5 can only be <6>
R2C1 is the only square in row 2 that can be <8>
R4C9 is the only square in row 4 that can be <6>
R5C3 is the only square in row 5 that can be <6>
R5C5 is the only square in row 5 that can be <7>
R5C7 is the only square in row 5 that can be <8>
R5C2 is the only square in row 5 that can be <9>
R2C5 is the only square in row 2 that can be <9>
R3C3 is the only square in row 3 that can be <9>
R7C7 is the only square in row 7 that can be <9>
R7C1 is the only square in column 1 that can be <1>
R5C9 is the only square in column 9 that can be <1>
Squares R6C9 and R7C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <4> from <2457> leaving <257>
R8C9 - removing <4> from <247> leaving <27>
Intersection of column 7 with block 3. The value <4> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <4> from <147> leaving <17>
Intersection of block 4 with column 1. The values <234> only appears in one or more of squares R4C1, R5C1 and R6C1 of block 4. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain these values.
R3C1 - removing <24> from <2457> leaving <57>
R8C1 - removing <24> from <2457> leaving <57>
R3C7 is the only square in row 3 that can be <4>
Squares R2C2 and R2C9 in row 2 and R8C2 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 9 can be removed.
R1C2 - removing <2> from <2457> leaving <457>
R3C9 - removing <2> from <257> leaving <57>
R9C2 - removing <2> from <27> leaving <7>
R8C1 can only be <5>
R3C1 can only be <7>
R3C9 can only be <5>
R3C5 can only be <2>
R2C9 can only be <2>
R2C2 can only be <5>
R8C9 can only be <7>
R1C7 can only be <1>
R1C4 can only be <3>
R8C8 can only be <4>
R1C5 can only be <5>
R5C4 can only be <2>
R1C2 can only be <4>
R1C8 can only be <7>
R9C7 can only be <2>
R8C2 can only be <2>
R5C8 can only be <3>
R7C9 can only be <3>
R9C3 can only be <3>
R1C3 can only be <2>
R5C1 can only be <4>
R9C8 can only be <1>
R6C9 can only be <4>
R6C5 can only be <3>
R7C3 can only be <4>
R4C1 can only be <3>
R6C1 can only be <2>
R4C5 can only be <4>
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