May 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C3 is the only square in row 4 that can be <2>
R6C4 is the only square in row 6 that can be <1>
R6C7 is the only square in row 6 that can be <3>
R4C4 is the only square in row 4 that can be <3>
R1C5 is the only square in row 1 that can be <3>
R7C1 is the only square in row 7 that can be <2>
R7C5 is the only square in row 7 that can be <8>
R8C9 is the only square in row 8 that can be <3>
R9C6 is the only square in row 9 that can be <2>
R2C1 is the only square in column 1 that can be <8>
R6C3 is the only square in column 3 that can be <8>
R6C8 can only be <4>
R7C9 is the only square in column 9 that can be <5>
R4C7 is the only square in column 7 that can be <5>
R4C2 can only be <4>
R4C6 can only be <8>
R4C8 can only be <6>
R5C8 can only be <8>
R1C7 is the only square in row 1 that can be <8>
R5C6 is the only square in column 6 that can be <4>
R2C7 is the only square in column 7 that can be <1>
Squares R5C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <59> from <1569> leaving <16>
R9C2 - removing <59> from <1569> leaving <16>
Squares R2C3 and R7C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <69> from <15679> leaving <157>
R3C3 - removing <69> from <5679> leaving <57>
R8C3 - removing <9> from <1459> leaving <145>
R9C3 - removing <69> from <14569> leaving <145>
Squares R2C9 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C7 - removing <46> from <4679> leaving <79>
Squares R3C1<59>, R3C3<57> and R3C7<79> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <579>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C5 - removing <59> from <4569> leaving <46>
Intersection of row 3 with block 1. The value <5> 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.
R1C3 - removing <5> from <157> leaving <17>
Squares R3C5, R3C9, R2C5 and R2C9 form a Type-1 Unique Rectangle on <46>.
R2C5 - removing <46> from <469> leaving <9>
R2C3 can only be <6>
R1C6 can only be <5>
R1C4 can only be <6>
R6C6 can only be <9>
R2C9 can only be <4>
R7C3 can only be <9>
R1C2 can only be <1>
R3C9 can only be <6>
R3C5 can only be <4>
R6C2 can only be <5>
R7C7 can only be <6>
R8C1 can only be <5>
R8C5 can only be <1>
R3C1 can only be <9>
R8C3 can only be <4>
R9C5 can only be <5>
R9C4 can only be <9>
R5C5 can only be <6>
R1C3 can only be <7>
R9C2 can only be <6>
R1C8 can only be <9>
R3C3 can only be <5>
R5C4 can only be <5>
R9C8 can only be <7>
R3C7 can only be <7>
R5C2 can only be <9>
R8C7 can only be <9>
R9C3 can only be <1>
R9C7 can only be <4>
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