Jun 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <4>
R2C6 is the only square in row 2 that can be <5>
R2C4 is the only square in row 2 that can be <8>
R4C2 is the only square in row 4 that can be <8>
R6C7 is the only square in row 6 that can be <5>
R7C5 is the only square in row 7 that can be <5>
R7C8 is the only square in row 7 that can be <8>
R7C7 is the only square in row 7 that can be <1>
R4C7 can only be <9>
R5C3 is the only square in row 5 that can be <9>
R8C3 is the only square in row 8 that can be <7>
R2C7 is the only square in row 2 that can be <7>
R3C2 is the only square in row 3 that can be <7>
R3C5 is the only square in row 3 that can be <9>
R1C5 can only be <6>
R9C5 can only be <7>
R1C2 is the only square in row 1 that can be <9>
R8C9 is the only square in row 8 that can be <9>
R9C1 is the only square in row 9 that can be <5>
Squares R3C4 and R3C6 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C3 - removing <24> from <1234> leaving <13>
R3C7 - removing <2> from <236> leaving <36>
R3C8 - removing <24> from <12346> leaving <136>
R2C3 is the only square in block 1 that can be <2>
Intersection of row 9 with block 9. The value <6> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <6> from <236> leaving <23>
Intersection of column 9 with block 3. The value <4> 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 <4> from <234> leaving <23>
Intersection of block 1 with column 1. The value <4> only appears in one or more of squares R1C1, R2C1 and R3C1 of block 1. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R8C1 - removing <4> from <346> leaving <36>
Intersection of row 8 with block 8. The value <4> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <4> from <246> leaving <26>
R7C6 - removing <4> from <234> leaving <23>
Squares R3C4, R3C6, R8C4 and R8C6 form a Type-3 Unique Rectangle on <24>. Upon close inspection, it is clear that:
(R8C4 or R8C6)<36> and R8C1<36> form a naked pair on <36> in row 8. No other squares in the row can contain these possibilities
R8C7 - removing <3> from <23> leaving <2>
R5C7 can only be <6>
R9C9 can only be <6>
R9C8 can only be <3>
R5C1 can only be <1>
R3C7 can only be <3>
R6C8 can only be <4>
R6C2 can only be <3>
R4C8 can only be <1>
R9C2 can only be <2>
R1C8 can only be <2>
R1C9 can only be <4>
R1C1 can only be <3>
R2C9 can only be <1>
R2C1 can only be <4>
R5C9 can only be <2>
R3C8 can only be <6>
R3C3 can only be <1>
R4C3 can only be <4>
R6C3 can only be <6>
R7C2 can only be <4>
R8C1 can only be <6>
R7C3 can only be <3>
R7C6 can only be <2>
R7C4 can only be <6>
R3C6 can only be <4>
R8C4 can only be <4>
R8C6 can only be <3>
R3C4 can only be <2>
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