Feb 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <3>
R9C7 can only be <8>
R6C7 can only be <3>
R7C7 can only be <6>
R3C7 can only be <4>
R3C6 is the only square in row 3 that can be <2>
R4C8 is the only square in row 4 that can be <4>
R4C9 is the only square in row 4 that can be <2>
R7C9 can only be <1>
R2C9 can only be <5>
R9C8 can only be <2>
R3C8 can only be <8>
R1C8 can only be <1>
R6C8 can only be <5>
R5C1 is the only square in row 5 that can be <3>
R7C2 is the only square in row 7 that can be <2>
R6C1 is the only square in column 1 that can be <1>
R9C1 is the only square in column 1 that can be <4>
R4C1 is the only square in column 1 that can be <8>
Squares R4C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <6> from <568> leaving <58>
R5C6 - removing <9> from <189> leaving <18>
R9C6 - removing <9> from <159> leaving <15>
Intersection of row 3 with block 1. The value <5> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <5> from <357> leaving <37>
Intersection of row 9 with block 8. The values <15> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <5> from <58> leaving <8>
R6C9 is the only square in row 6 that can be <8>
R5C9 can only be <9>
R5C4 can only be <1>
R5C6 can only be <8>
R1C6 can only be <5>
R9C6 can only be <1>
R1C5 is the only square in row 1 that can be <8>
R2C5 is the only square in row 2 that can be <1>
R9C4 is the only square in row 9 that can be <5>
Intersection of column 1 with block 7. The value <7> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <7> from <357> leaving <35>
Squares R2C2 and R2C4 in row 2 and R6C2 and R6C4 in row 6 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 4 can be removed.
R4C2 - removing <9> from <679> leaving <67>
R9C2 - removing <9> from <39> leaving <3>
R9C5 can only be <9>
R7C3 can only be <5>
R3C5 can only be <6>
R8C6 can only be <6>
R3C9 can only be <3>
R8C5 can only be <7>
R1C4 can only be <4>
R1C9 can only be <6>
R7C1 can only be <7>
R3C3 can only be <9>
R8C1 can only be <9>
R7C5 can only be <3>
R4C6 can only be <9>
R1C2 can only be <7>
R2C4 can only be <9>
R2C2 can only be <4>
R6C4 can only be <6>
R3C1 can only be <5>
R4C3 can only be <7>
R4C2 can only be <6>
R1C3 can only be <3>
R6C2 can only be <9>
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