Jun 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <1>
R2C1 is the only square in row 2 that can be <1>
R2C9 is the only square in row 2 that can be <8>
R6C9 can only be <1>
R2C7 is the only square in row 2 that can be <9>
R3C5 is the only square in row 3 that can be <2>
R5C4 is the only square in row 5 that can be <1>
R7C7 is the only square in row 7 that can be <1>
R1C4 is the only square in column 4 that can be <7>
Squares R3C7 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <45> from <4567> leaving <67>
R3C3 - removing <45> from <4567> leaving <67>
R2C3 is the only square in column 3 that can be <4>
R1C2 can only be <5>
R1C6 can only be <4>
R5C3 is the only square in column 3 that can be <5>
R5C6 can only be <8>
R5C7 can only be <3>
R5C5 can only be <7>
R8C7 can only be <4>
R3C7 can only be <5>
R3C8 can only be <4>
R9C4 is the only square in row 9 that can be <4>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <5> from <356> leaving <36>
R8C5 - removing <5> from <3568> leaving <368>
Squares R4C9 and R5C8 in block 6 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 block.
R4C8 - removing <69> from <5689> leaving <58>
Intersection of row 8 with block 8. The values <35> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C5 - removing <3> from <368> leaving <68>
R9C6 - removing <3> from <39> leaving <9>
Intersection of column 3 with block 7. The value <9> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <9> from <3689> leaving <368>
Squares R5C2 and R5C8 in row 5 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C2 - removing <6> from <67> leaving <7>
R4C2 - removing <6> from <4689> leaving <489>
R7C2 - removing <6> from <368> leaving <38>
R7C8 - removing <6> from <369> leaving <39>
R3C3 can only be <6>
R7C3 can only be <9>
R7C8 can only be <3>
R8C3 can only be <7>
R7C2 can only be <8>
R9C8 can only be <6>
R9C2 can only be <3>
R5C8 can only be <9>
R8C9 can only be <9>
R5C2 can only be <6>
R4C9 can only be <6>
R7C5 can only be <6>
R6C2 can only be <4>
R8C1 can only be <6>
R2C5 can only be <3>
R8C4 can only be <5>
R4C1 can only be <8>
R8C6 can only be <3>
R2C4 can only be <6>
R8C5 can only be <8>
R2C6 can only be <5>
R4C8 can only be <5>
R6C1 can only be <7>
R4C5 can only be <4>
R6C8 can only be <8>
R6C5 can only be <5>
R4C2 can only be <9>
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