Mar 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <8>
R5C7 can only be <6>
R5C8 can only be <2>
R6C2 can only be <5>
R5C9 can only be <5>
R6C8 can only be <1>
R6C4 can only be <2>
R6C6 can only be <9>
R5C5 can only be <4>
R4C2 is the only square in row 4 that can be <6>
R5C3 is the only square in row 5 that can be <9>
R7C6 is the only square in row 7 that can be <1>
R8C6 is the only square in row 8 that can be <2>
R7C1 is the only square in column 1 that can be <5>
R7C9 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <6>
R3C1 is the only square in row 3 that can be <6>
R7C8 is the only square in row 7 that can be <9>
R3C9 is the only square in row 3 that can be <9>
R7C7 is the only square in row 7 that can be <4>
R2C4 is the only square in row 2 that can be <4>
R9C1 is the only square in row 9 that can be <2>
R9C5 is the only square in row 9 that can be <9>
R8C5 is the only square in column 5 that can be <5>
Squares R7C4 and R8C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C4 - removing <78> from <3578> leaving <35>
Intersection of block 9 with row 9. The value <7> only appears in one or more of squares R9C7, R9C8 and R9C9 of block 9. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C2 - removing <7> from <378> leaving <38>
Squares R1C1<37>, R2C3<378> and R3C3<378> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <378>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C2 - removing <378> from <13478> leaving <14>
R3C2 - removing <378> from <13478> leaving <14>
Intersection of column 2 with block 7. The value <8> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <8> from <378> leaving <37>
Squares R1C1 and R1C8 in row 1, R5C1 and R5C2 in row 5 and R9C2 and R9C8 in row 9 form a Swordfish pattern on possibility <3>. All other instances of this possibility in columns 1, 2 and 8 can be removed.
R3C8 - removing <3> from <347> leaving <47>
Squares R4C4, R4C6, R3C4 and R3C6 form a Type-1 Unique Rectangle on <35>.
R3C6 - removing <35> from <357> leaving <7>
R3C8 can only be <4>
R2C6 can only be <3>
R3C2 can only be <1>
R4C6 can only be <5>
R3C4 can only be <5>
R1C2 can only be <4>
R4C4 can only be <3>
R1C5 is the only square in row 1 that can be <1>
R2C5 can only be <8>
R2C3 can only be <7>
R2C7 can only be <1>
R8C3 can only be <3>
R1C1 can only be <3>
R8C7 can only be <8>
R3C3 can only be <8>
R9C2 can only be <8>
R8C4 can only be <7>
R3C7 can only be <3>
R9C9 can only be <7>
R7C2 can only be <7>
R9C8 can only be <3>
R1C9 can only be <8>
R1C8 can only be <7>
R5C1 can only be <7>
R5C2 can only be <3>
R7C4 can only be <8>
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