Apr 11 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <9>
R2C3 is the only square in row 2 that can be <4>
R3C3 is the only square in row 3 that can be <3>
R6C5 is the only square in row 6 that can be <4>
R7C2 is the only square in row 7 that can be <4>
R7C3 is the only square in row 7 that can be <5>
R9C9 is the only square in row 9 that can be <2>
R1C1 is the only square in row 1 that can be <2>
R2C7 is the only square in row 2 that can be <2>
R5C1 is the only square in column 1 that can be <9>
R5C2 is the only square in column 2 that can be <5>
R9C2 is the only square in column 2 that can be <7>
R8C3 is the only square in column 3 that can be <8>
R2C1 is the only square in column 1 that can be <8>
R4C4 is the only square in column 4 that can be <5>
Squares R1C5 and R2C5 in column 5 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 column.
R4C5 - removing <1> from <136> leaving <36>
R5C5 - removing <1> from <13678> leaving <3678>
R8C5 - removing <1> from <137> leaving <37>
R9C5 - removing <1> from <138> leaving <38>
Squares R1C5 and R2C5 in block 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 block.
R3C4 - removing <1> from <128> leaving <28>
R3C6 - removing <1> from <128> leaving <28>
Intersection of block 8 with row 7. The value <1> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C7 - removing <1> from <137> leaving <37>
R7C8 - removing <1> from <178> leaving <78>
Squares R4C6<19>, R6C4<12> and R6C6<129> in block 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <129>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C4 - removing <1> from <138> leaving <38>
R5C6 - removing <1> from <178> leaving <78>
Intersection of row 5 with block 6. The value <1> 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.
R4C7 - removing <1> from <1369> leaving <369>
R6C7 - removing <1> from <169> leaving <69>
Squares R2C5, R2C9, R1C5 and R1C9 form a Type-1 Unique Rectangle on <15>.
R1C9 - removing <15> from <156> leaving <6>
R1C2 can only be <1>
R1C5 can only be <5>
R3C2 can only be <6>
R2C5 can only be <1>
R2C9 can only be <5>
R8C7 is the only square in row 8 that can be <6>
R6C7 can only be <9>
R4C7 can only be <3>
R4C5 can only be <6>
R7C7 can only be <7>
R5C9 can only be <1>
R5C8 can only be <6>
R8C9 can only be <3>
R7C8 can only be <8>
R3C7 can only be <1>
R7C6 can only be <1>
R9C8 can only be <1>
R8C1 can only be <1>
R8C5 can only be <7>
R9C1 can only be <3>
R3C8 can only be <7>
R4C3 can only be <1>
R7C4 can only be <3>
R4C6 can only be <9>
R6C6 can only be <2>
R9C5 can only be <8>
R5C5 can only be <3>
R6C3 can only be <6>
R5C4 can only be <8>
R6C4 can only be <1>
R3C6 can only be <8>
R3C4 can only be <2>
R5C6 can only be <7>
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