Jun 18 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C8 can only be <5>
R2C6 is the only square in row 2 that can be <9>
R3C6 is the only square in row 3 that can be <3>
R9C1 is the only square in row 9 that can be <7>
R8C6 is the only square in column 6 that can be <4>
Intersection of row 3 with block 1. The value <2> 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.
R2C1 - removing <2> from <24568> leaving <4568>
R2C2 - removing <2> from <2567> leaving <567>
Intersection of row 3 with block 3. The value <1> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <1> from <1467> leaving <467>
Intersection of row 9 with block 8. The value <5> 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 this value.
R8C4 - removing <5> from <23568> leaving <2368>
R8C5 - removing <5> from <235> leaving <23>
Intersection of column 6 with block 5. The value <6> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <6> from <3568> leaving <358>
R6C4 - removing <6> from <13567> leaving <1357>
Intersection of column 8 with block 9. The value <9> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C9 - removing <9> from <2689> leaving <268>
Squares R1C3<57>, R1C4<157> and R1C6<15> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <157>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <5> from <456> leaving <46>
R1C9 - removing <7> from <467> leaving <46>
R3C9 is the only square in column 9 that can be <7>
R3C2 can only be <2>
R3C3 can only be <8>
R7C2 can only be <9>
R3C7 can only be <1>
R8C2 can only be <5>
R2C7 is the only square in row 2 that can be <8>
R6C9 is the only square in row 6 that can be <9>
R5C3 is the only square in row 5 that can be <9>
R6C4 is the only square in row 6 that can be <1>
R4C6 can only be <6>
R1C6 is the only square in row 1 that can be <1>
R4C9 is the only square in row 4 that can be <1>
R4C8 is the only square in row 4 that can be <4>
R2C8 can only be <6>
R2C2 can only be <7>
R7C8 can only be <3>
R1C9 can only be <4>
R7C3 can only be <2>
R8C8 can only be <9>
R9C7 can only be <2>
R9C9 can only be <8>
R9C6 can only be <5>
R8C9 can only be <6>
R1C1 can only be <6>
R6C2 can only be <6>
R1C3 can only be <5>
R6C7 can only be <3>
R6C1 can only be <5>
R5C7 can only be <6>
R7C1 can only be <8>
R8C3 can only be <3>
R8C5 can only be <2>
R4C3 can only be <7>
R2C5 can only be <5>
R8C4 can only be <8>
R5C9 can only be <2>
R7C7 can only be <4>
R9C4 can only be <3>
R5C6 can only be <8>
R1C4 can only be <7>
R2C1 can only be <4>
R2C4 can only be <2>
R6C5 can only be <7>
R4C5 can only be <3>
R4C1 can only be <2>
R5C4 can only be <5>
R5C1 can only be <3>
R7C4 can only be <6>
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