Oct 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C4 can only be <2>
R7C5 can only be <7>
R9C1 can only be <8>
R8C4 can only be <8>
R8C6 can only be <9>
R9C5 can only be <2>
R2C4 is the only square in row 2 that can be <3>
R4C4 can only be <6>
R5C4 can only be <7>
R2C6 is the only square in row 2 that can be <6>
R4C5 is the only square in row 4 that can be <3>
R5C9 is the only square in row 5 that can be <6>
R5C6 is the only square in column 6 that can be <8>
Squares R1C5 and R3C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <1> from <149> leaving <49>
R6C5 - removing <1> from <149> leaving <49>
Intersection of row 5 with block 4. The value <1> 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.
R4C2 - removing <1> from <159> leaving <59>
R6C2 - removing <1> from <1459> leaving <459>
Intersection of column 9 with block 3. The value <1> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. 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 <1> from <1478> leaving <478>
R2C8 - removing <1> from <124789> leaving <24789>
R3C8 - removing <1> from <189> leaving <89>
Squares R5C3 and R8C3 in column 3 and R5C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C1 - removing <5> from <1459> leaving <149>
R8C1 - removing <5> from <15> leaving <1>
R8C2 - removing <5> from <1357> leaving <137>
R8C8 - removing <5> from <2457> leaving <247>
R5C3 is the only square in row 5 that can be <1>
R2C3 can only be <7>
R8C3 can only be <5>
R8C7 can only be <4>
R7C2 can only be <6>
R2C7 can only be <9>
R2C1 can only be <4>
R5C7 can only be <5>
R3C8 can only be <8>
R3C5 can only be <1>
R7C8 can only be <5>
R2C8 can only be <2>
R1C1 can only be <5>
R5C1 can only be <9>
R2C9 can only be <1>
R8C8 can only be <7>
R2C2 can only be <8>
R1C9 can only be <7>
R3C2 can only be <9>
R1C5 can only be <8>
R5C5 can only be <4>
R4C2 can only be <5>
R6C5 can only be <9>
R6C8 can only be <1>
R6C6 can only be <5>
R4C8 can only be <9>
R8C2 can only be <3>
R1C8 can only be <4>
R9C8 can only be <6>
R9C9 can only be <3>
R9C2 can only be <7>
R8C9 can only be <2>
R1C2 can only be <1>
R4C6 can only be <1>
R6C2 can only be <4>
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