Nov 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C3 can only be <2>
R8C7 can only be <4>
R8C1 can only be <9>
R8C9 can only be <8>
R8C5 can only be <6>
R2C5 can only be <7>
R3C5 can only be <2>
R2C3 can only be <6>
R1C7 is the only square in row 1 that can be <2>
R1C3 is the only square in row 1 that can be <7>
R3C8 is the only square in row 3 that can be <6>
R4C6 is the only square in row 4 that can be <2>
R7C9 is the only square in row 7 that can be <7>
R6C1 is the only square in column 1 that can be <7>
R6C6 can only be <6>
R6C4 can only be <1>
R1C6 can only be <8>
R1C4 can only be <6>
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.
R2C7 - removing <1> from <15> leaving <5>
Intersection of block 4 with row 5. The value <5> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C5 - removing <5> from <3459> leaving <349>
Squares R5C3 and R9C3 in column 3 and R5C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <3> from <358> leaving <58>
R9C2 - removing <3> from <1345> leaving <145>
R5C5 - removing <3> from <349> leaving <49>
R5C8 - removing <3> from <134> leaving <14>
R9C8 - removing <3> from <139> leaving <19>
Squares R5C5 and R7C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <4> from <345> leaving <35>
Squares R6C5, R6C9, R4C5 and R4C9 form a Type-1 Unique Rectangle on <35>.
R4C9 - removing <35> from <345> leaving <4>
R4C4 can only be <8>
R2C9 can only be <1>
R5C8 can only be <1>
R5C7 can only be <3>
R9C8 can only be <9>
R9C6 can only be <7>
R7C8 can only be <3>
R2C1 can only be <4>
R3C9 can only be <3>
R6C9 can only be <5>
R1C8 can only be <4>
R4C1 can only be <3>
R5C3 can only be <5>
R9C7 can only be <1>
R6C5 can only be <3>
R9C4 can only be <4>
R5C6 can only be <9>
R1C2 can only be <3>
R7C1 can only be <1>
R4C5 can only be <5>
R5C2 can only be <8>
R9C3 can only be <3>
R5C5 can only be <4>
R7C2 can only be <4>
R3C1 can only be <8>
R7C5 can only be <9>
R9C2 can only be <5>
R5C4 can only be <7>
R3C2 can only be <1>
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