Aug 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <7>
R6C7 can only be <2>
R1C5 can only be <3>
R6C3 can only be <7>
R9C5 can only be <5>
R9C8 can only be <6>
R1C7 is the only square in row 1 that can be <6>
R1C2 is the only square in row 1 that can be <7>
R5C9 is the only square in row 5 that can be <6>
R5C7 is the only square in row 5 that can be <3>
R9C7 can only be <9>
R7C3 is the only square in row 7 that can be <9>
R7C4 is the only square in row 7 that can be <6>
R8C4 can only be <4>
R8C6 can only be <3>
R7C6 can only be <1>
R8C3 is the only square in row 8 that can be <6>
R7C9 is the only square in column 9 that can be <3>
R7C2 can only be <2>
R8C9 is the only square in row 8 that can be <2>
Squares R7C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <5> from <158> leaving <18>
R3C1 - removing <5> from <1258> leaving <128>
Squares R2C9 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C7 - removing <7> from <1578> leaving <158>
R3C7 - removing <7> from <1578> leaving <158>
Squares R1C3<28>, R2C1<18> and R3C1<128> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <128>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <18> from <1458> leaving <45>
R3C2 - removing <1> from <134> leaving <34>
R3C3 - removing <128> from <123458> leaving <345>
Intersection of block 1 with column 1. The value <1> 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.
R5C1 - removing <1> from <128> leaving <28>
Squares R8C1, R8C7, R7C1 and R7C7 form a Type-1 Unique Rectangle on <57>.
R7C7 - removing <57> from <457> leaving <4>
R7C8 can only be <5>
R4C7 can only be <8>
R7C1 can only be <7>
R8C7 can only be <7>
R8C1 can only be <5>
R4C3 can only be <4>
R5C8 can only be <4>
R5C2 can only be <1>
R2C3 can only be <5>
R9C2 can only be <3>
R9C3 can only be <1>
R3C2 can only be <4>
R2C7 can only be <1>
R3C3 can only be <3>
R2C1 can only be <8>
R3C7 can only be <5>
R3C6 can only be <7>
R3C9 can only be <9>
R2C6 can only be <4>
R3C4 can only be <8>
R2C9 can only be <7>
R2C4 can only be <9>
R5C1 can only be <2>
R1C3 can only be <2>
R3C8 can only be <2>
R3C1 can only be <1>
R1C8 can only be <8>
R5C3 can only be <8>
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