Apr 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <8>
R3C5 is the only square in row 3 that can be <3>
R5C5 can only be <7>
R7C5 can only be <6>
R7C3 can only be <8>
R7C8 can only be <7>
R9C5 can only be <1>
R1C5 can only be <2>
R5C3 can only be <4>
R4C9 is the only square in row 4 that can be <7>
R5C7 is the only square in row 5 that can be <8>
R6C1 is the only square in row 6 that can be <2>
R6C8 is the only square in row 6 that can be <4>
R1C2 is the only square in column 2 that can be <4>
R1C1 is the only square in row 1 that can be <7>
R2C7 is the only square in row 2 that can be <7>
R8C6 is the only square in row 8 that can be <7>
R8C4 is the only square in row 8 that can be <4>
R2C6 is the only square in row 2 that can be <4>
R9C2 is the only square in row 9 that can be <7>
R1C6 is the only square in column 6 that can be <5>
R1C8 can only be <1>
R1C4 can only be <9>
R2C4 can only be <1>
R6C6 is the only square in row 6 that can be <9>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <3> from <369> leaving <69>
R9C9 - removing <3> from <2369> leaving <269>
Squares R2C1 and R9C1 in column 1 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.
R8C1 - removing <6> from <136> leaving <13>
Intersection of column 7 with block 9. The value <3> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. 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 <3> from <356> leaving <56>
Squares R5C9<35>, R6C9<36> and R8C9<56> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <356>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C9 - removing <6> from <269> leaving <29>
Squares R9C4, R9C6, R4C4 and R4C6 form a Type-1 Unique Rectangle on <38>.
R4C4 - removing <38> from <368> leaving <6>
R4C8 can only be <5>
R3C8 can only be <2>
R5C9 can only be <3>
R5C1 can only be <5>
R6C9 can only be <6>
R8C9 can only be <5>
R8C7 can only be <3>
R3C3 can only be <1>
R9C8 can only be <6>
R2C9 can only be <9>
R8C1 can only be <1>
R7C7 can only be <9>
R9C1 can only be <9>
R2C1 can only be <6>
R9C9 can only be <2>
R3C7 can only be <5>
R3C2 can only be <9>
R8C3 can only be <6>
R7C2 can only be <3>
R4C1 can only be <3>
R2C3 can only be <2>
R4C6 can only be <8>
R6C2 can only be <8>
R4C2 can only be <1>
R9C6 can only be <3>
R6C4 can only be <3>
R9C4 can only be <8>
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