Nov 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <9>
R1C2 is the only square in row 1 that can be <1>
R1C8 is the only square in row 1 that can be <4>
R1C5 is the only square in row 1 that can be <6>
R2C6 is the only square in row 2 that can be <1>
R2C8 is the only square in row 2 that can be <8>
R2C2 is the only square in row 2 that can be <9>
R5C8 is the only square in row 5 that can be <1>
R5C4 is the only square in row 5 that can be <6>
R7C2 is the only square in row 7 that can be <7>
R8C7 is the only square in row 8 that can be <1>
R8C4 is the only square in column 4 that can be <8>
R6C4 is the only square in column 4 that can be <4>
R5C2 is the only square in row 5 that can be <4>
Squares R9C1 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C2 - removing <35> from <3568> leaving <68>
R9C3 - removing <35> from <3458> leaving <48>
R9C5 - removing <35> from <3459> leaving <49>
R9C7 - removing <3> from <2369> leaving <269>
R9C8 - removing <35> from <23569> leaving <269>
Squares R7C8 and R9C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <35> from <3569> leaving <69>
Intersection of row 1 with block 1. The value <5> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C3 - removing <5> from <2357> leaving <237>
Intersection of row 5 with block 5. The value <2> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <2> from <2359> leaving <359>
R5C6 is the only square in column 6 that can be <2>
Intersection of column 5 with block 8. The values <49> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C6 - removing <9> from <359> leaving <35>
Squares R7C5 and R8C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <35> from <3459> leaving <49>
Squares R5C1<357>, R6C2<35> and R6C3<357> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <35> from <2358> leaving <28>
R4C3 - removing <357> from <23578> leaving <28>
Squares R5C1 and R9C1 in column 1 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C5 - removing <3> from <357> leaving <57>
R7C5 is the only square in column 5 that can be <3>
R7C8 can only be <5>
R8C6 can only be <5>
R9C9 can only be <3>
R9C1 can only be <5>
R5C9 can only be <5>
R5C5 can only be <7>
R1C1 can only be <7>
R1C7 can only be <2>
R5C1 can only be <3>
R1C3 can only be <5>
R6C2 can only be <5>
R3C5 can only be <2>
R4C4 can only be <5>
R6C3 can only be <7>
R3C2 can only be <3>
R2C5 can only be <5>
R2C4 can only be <7>
R2C7 can only be <3>
R2C3 can only be <2>
R3C8 can only be <7>
R8C2 can only be <6>
R8C8 can only be <9>
R9C2 can only be <8>
R8C5 can only be <4>
R4C8 can only be <3>
R9C7 can only be <6>
R9C3 can only be <4>
R4C2 can only be <2>
R9C5 can only be <9>
R8C3 can only be <3>
R9C8 can only be <2>
R6C7 can only be <9>
R4C3 can only be <8>
R4C6 can only be <9>
R6C8 can only be <6>
R6C6 can only be <3>
R4C7 can only be <7>
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