Jun 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 is the only square in row 4 that can be <5>
R5C8 is the only square in row 5 that can be <3>
R5C2 is the only square in row 5 that can be <9>
R6C1 is the only square in row 6 that can be <6>
R7C1 is the only square in row 7 that can be <3>
R7C7 is the only square in row 7 that can be <9>
R2C9 is the only square in row 2 that can be <9>
R8C6 is the only square in row 8 that can be <2>
R8C9 is the only square in row 8 that can be <6>
R8C3 is the only square in row 8 that can be <9>
R5C1 is the only square in column 1 that can be <2>
Squares R4C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <1> from <123> leaving <23>
R2C3 - removing <1> from <136> leaving <36>
R3C3 - removing <1> from <1236> leaving <236>
Squares R8C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <8> from <2348> leaving <234>
R2C7 - removing <8> from <348> leaving <34>
R6C7 - removing <8> from <248> leaving <24>
Squares R8C7 and R9C7 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <8> from <178> leaving <17>
R9C8 - removing <8> from <178> leaving <17>
Squares R9C3 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <1> from <145> leaving <45>
R9C5 - removing <7> from <4578> leaving <458>
Squares R8C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <1> from <148> leaving <48>
R4C8 - removing <7> from <478> leaving <48>
Intersection of row 7 with block 8. The values <157> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C4 - removing <157> from <14578> leaving <48>
R9C5 - removing <5> from <458> leaving <48>
Squares R1C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C5 - removing <8> from <68> leaving <6>
R5C5 - removing <8> from <5678> leaving <567>
R2C3 is the only square in row 2 that can be <6>
R5C6 is the only square in row 5 that can be <6>
Squares R2C6 and R4C6 in column 6 and R2C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 4 can be removed.
R2C4 - removing <4> from <13478> leaving <1378>
R2C7 - removing <4> from <34> leaving <3>
R1C3 is the only square in row 1 that can be <3>
R3C3 can only be <2>
R3C4 is the only square in row 3 that can be <3>
Squares R2C1 and R4C1 in column 1 and R2C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 4 can be removed.
R2C2 - removing <8> from <158> leaving <15>
R2C4 - removing <8> from <178> leaving <17>
R2C6 - removing <8> from <1478> leaving <147>
R4C6 - removing <8> from <478> leaving <47>
R3C6 is the only square in column 6 that can be <8>
R3C9 can only be <1>
R1C5 can only be <4>
R1C7 can only be <2>
R9C5 can only be <8>
R1C9 can only be <8>
R6C7 can only be <4>
R1C2 can only be <1>
R5C9 can only be <7>
R2C8 can only be <4>
R4C8 can only be <8>
R4C1 can only be <1>
R5C5 can only be <5>
R6C9 can only be <2>
R9C7 can only be <5>
R8C4 can only be <4>
R9C1 can only be <4>
R8C7 can only be <8>
R2C2 can only be <5>
R2C1 can only be <8>
R8C2 can only be <7>
R4C3 can only be <7>
R4C6 can only be <4>
R9C3 can only be <1>
R6C2 can only be <8>
R5C4 can only be <8>
R7C5 can only be <7>
R6C4 can only be <7>
R2C4 can only be <1>
R7C6 can only be <1>
R7C4 can only be <5>
R2C6 can only be <7>
R8C8 can only be <1>
R8C1 can only be <5>
R9C8 can only be <7>
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