Jun 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C2 can only be <4>
R7C5 can only be <5>
R6C6 is the only square in row 6 that can be <8>
R5C5 can only be <1>
R5C3 is the only square in row 5 that can be <8>
R8C8 is the only square in row 8 that can be <8>
R3C8 can only be <4>
R3C5 can only be <8>
R1C5 can only be <4>
R2C5 can only be <9>
R1C9 is the only square in row 1 that can be <8>
R2C3 is the only square in row 2 that can be <4>
R1C1 is the only square in column 1 that can be <7>
R1C3 is the only square in column 3 that can be <6>
R1C2 is the only square in row 1 that can be <2>
R2C2 can only be <3>
R1C7 is the only square in row 1 that can be <3>
R2C8 is the only square in row 2 that can be <2>
Squares R2C7 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C4 - removing <15> from <1567> leaving <67>
R2C6 - removing <15> from <1567> leaving <67>
Intersection of row 5 with block 6. The value <5> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <5> from <357> leaving <37>
R4C9 - removing <5> from <145> leaving <14>
Squares R4C8<37>, R5C7<56>, R5C8<567> and R6C8<36> in block 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C7 - removing <6> from <146> leaving <14>
Squares R2C4, R2C6, R9C4 and R9C6 form a Type-4 Unique Rectangle on <67>.
R9C4 - removing <6> from <1467> leaving <147>
R9C6 - removing <6> from <1467> leaving <147>
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 <4569> leaving <459>
Squares R8C5, R9C5, R8C3 and R9C3 form a Type-2 Unique Rectangle on <23>.
R4C3 - removing <1> from <13> leaving <3>
R8C2 - removing <1> from <19> leaving <9>
R4C8 can only be <7>
R6C1 can only be <9>
R6C4 can only be <4>
R4C2 can only be <1>
R6C7 can only be <1>
R4C6 can only be <5>
R6C2 can only be <6>
R2C7 can only be <5>
R4C9 can only be <4>
R2C9 can only be <1>
R5C7 can only be <6>
R8C7 can only be <4>
R4C4 can only be <9>
R1C6 can only be <1>
R9C9 can only be <5>
R5C2 can only be <7>
R5C8 can only be <5>
R6C8 can only be <3>
R9C8 can only be <6>
R9C7 can only be <9>
R9C1 can only be <3>
R1C4 can only be <5>
R8C6 can only be <6>
R8C4 can only be <1>
R2C6 can only be <7>
R9C5 can only be <2>
R8C1 can only be <5>
R9C3 can only be <1>
R8C5 can only be <3>
R2C4 can only be <6>
R9C6 can only be <4>
R8C3 can only be <2>
R9C4 can only be <7>
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