Jun 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <3>
R2C3 is the only square in row 2 that can be <3>
R2C7 is the only square in row 2 that can be <2>
R4C4 is the only square in row 4 that can be <2>
R4C3 is the only square in row 4 that can be <1>
R5C8 is the only square in row 5 that can be <2>
R6C4 is the only square in row 6 that can be <1>
R3C4 can only be <7>
R7C4 can only be <8>
R2C1 is the only square in row 2 that can be <7>
R5C9 is the only square in row 5 that can be <1>
R6C7 is the only square in row 6 that can be <3>
R7C2 is the only square in row 7 that can be <1>
R1C1 is the only square in row 1 that can be <1>
R3C5 is the only square in row 3 that can be <1>
R9C2 is the only square in column 2 that can be <6>
R9C5 is the only square in row 9 that can be <2>
R8C3 is the only square in row 8 that can be <2>
R3C2 is the only square in row 3 that can be <2>
R9C9 is the only square in row 9 that can be <7>
Squares R8C5 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C7 - removing <56> from <4568> leaving <48>
Squares R4C7 and R5C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C7 - removing <9> from <4689> leaving <468>
R7C7 - removing <59> from <4569> leaving <46>
Intersection of column 9 with block 3. The value <9> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <9> from <589> leaving <58>
R3C8 - removing <9> from <489> leaving <48>
Intersection of block 7 with column 1. The value <8> only appears in one or more of squares R7C1, R8C1 and R9C1 of block 7. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R5C1 - removing <8> from <489> leaving <49>
Squares R2C5 and R2C9 in row 2 and R8C5 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 5 and 9 can be removed.
R7C5 - removing <6> from <567> leaving <57>
Squares R3C3 and R3C6 in row 3 and R6C3 and R6C6 in row 6 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 6 can be removed.
R4C6 - removing <9> from <59> leaving <5>
R5C3 - removing <9> from <4789> leaving <478>
R7C3 - removing <9> from <49> leaving <4>
R4C7 can only be <9>
R5C7 can only be <5>
R7C7 can only be <6>
R8C1 can only be <8>
R7C6 can only be <7>
R8C9 can only be <5>
R8C7 can only be <4>
R9C1 can only be <9>
R3C7 can only be <8>
R8C5 can only be <6>
R1C9 can only be <9>
R7C8 can only be <9>
R9C8 can only be <8>
R5C1 can only be <4>
R1C8 can only be <5>
R3C8 can only be <4>
R1C2 can only be <8>
R2C9 can only be <6>
R2C5 can only be <9>
R3C3 can only be <9>
R7C5 can only be <5>
R6C6 can only be <9>
R5C2 can only be <9>
R5C5 can only be <7>
R3C6 can only be <6>
R6C3 can only be <7>
R5C3 can only be <8>
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