Jun 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 can only be <8>
R3C1 can only be <3>
R3C7 can only be <1>
R3C5 can only be <6>
R3C9 can only be <7>
R1C2 is the only square in row 1 that can be <6>
R1C6 is the only square in row 1 that can be <7>
R1C4 is the only square in row 1 that can be <2>
R1C5 is the only square in row 1 that can be <1>
R6C9 is the only square in row 6 that can be <6>
R6C2 is the only square in row 6 that can be <7>
R9C8 is the only square in row 9 that can be <7>
R5C5 is the only square in column 5 that can be <5>
Squares R5C4 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <3> from <1238> leaving <128>
R5C9 - removing <3> from <138> leaving <18>
Intersection of row 1 with block 1. The value <4> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <4> from <459> leaving <59>
Intersection of row 1 with block 3. The values <38> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C8 - removing <38> from <3589> leaving <59>
Intersection of column 3 with block 7. The value <2> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <2> from <12489> leaving <1489>
R9C1 - removing <2> from <124589> leaving <14589>
Intersection of column 7 with block 9. The value <2> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C8 - removing <2> from <1258> leaving <158>
R8C6 is the only square in row 8 that can be <2>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C8 - removing <5> from <3589> leaving <389>
R4C2 - removing <5> from <15> leaving <1>
R4C8 - removing <5> from <1235> leaving <123>
R6C8 - removing <5> from <58> leaving <8>
R9C2 - removing <5> from <14589> leaving <1489>
R6C1 can only be <5>
R5C9 can only be <1>
R5C8 can only be <2>
R4C1 can only be <2>
R4C8 can only be <3>
R4C9 can only be <5>
R1C8 can only be <9>
R1C1 can only be <4>
R2C8 can only be <5>
R2C2 can only be <9>
R8C8 can only be <1>
R1C7 can only be <8>
R8C4 can only be <8>
R1C3 can only be <5>
R5C1 can only be <8>
R1C9 can only be <3>
R7C7 can only be <2>
R5C2 can only be <4>
R9C2 can only be <8>
R7C3 can only be <4>
R9C7 can only be <5>
R8C2 can only be <5>
R8C5 can only be <4>
R2C4 can only be <3>
R7C5 can only be <9>
R9C9 can only be <4>
R9C3 can only be <2>
R7C9 can only be <8>
R2C5 can only be <8>
R2C6 can only be <4>
R5C4 can only be <6>
R5C6 can only be <3>
R9C4 can only be <1>
R9C6 can only be <6>
R7C1 can only be <1>
R9C5 can only be <3>
R9C1 can only be <9>
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