May 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 is the only square in row 5 that can be <9>
R3C4 can only be <5>
R2C4 can only be <6>
R8C4 can only be <8>
R6C4 can only be <7>
R9C5 can only be <4>
R7C6 can only be <7>
R8C6 can only be <5>
R8C5 can only be <6>
R1C9 is the only square in row 1 that can be <6>
R1C7 is the only square in row 1 that can be <8>
R3C2 is the only square in row 3 that can be <9>
R1C2 can only be <2>
R1C5 can only be <9>
R3C3 can only be <3>
R2C5 can only be <2>
R2C6 can only be <1>
R2C9 can only be <3>
R2C7 can only be <5>
R9C3 can only be <7>
R2C8 can only be <9>
R7C3 is the only square in row 7 that can be <6>
R8C1 is the only square in row 8 that can be <9>
R5C3 is the only square in column 3 that can be <1>
R6C7 is the only square in column 7 that can be <3>
R3C7 is the only square in column 7 that can be <1>
R3C9 can only be <2>
Squares R4C3 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <24> from <234578> leaving <3578>
R4C2 - removing <4> from <34678> leaving <3678>
R4C8 - removing <2> from <2568> leaving <568>
R4C9 - removing <4> from <478> leaving <78>
Squares R5C6 and R5C7 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C1 - removing <24> from <24578> leaving <578>
R5C2 - removing <4> from <4678> leaving <678>
R5C8 - removing <2> from <2568> leaving <568>
R5C9 - removing <4> from <478> leaving <78>
Squares R4C9 and R5C9 in column 9 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.
R6C9 - removing <8> from <148> leaving <14>
Squares R4C9 and R5C9 in block 6 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 block.
R4C8 - removing <8> from <568> leaving <56>
R5C8 - removing <8> from <568> leaving <56>
R6C8 - removing <8> from <1258> leaving <125>
Squares R4C8 and R5C8 in column 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 column.
R6C8 - removing <5> from <125> leaving <12>
Intersection of column 2 with block 4. The values <68> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C1 - removing <8> from <3578> leaving <357>
R5C1 - removing <8> from <578> leaving <57>
R6C1 - removing <8> from <2458> leaving <245>
Squares R7C7 and R8C3 form a remote naked pair. <24> can be removed from any square that is common to their groups.
R8C8 - removing <2> from <123> leaving <13>
R8C9 - removing <4> from <14> leaving <1>
R7C1 - removing <24> from <248> leaving <8>
R7C8 can only be <2>
R9C1 can only be <3>
R7C7 can only be <4>
R6C8 can only be <1>
R8C8 can only be <3>
R6C9 can only be <4>
R9C8 can only be <8>
R8C2 can only be <4>
R6C2 can only be <8>
R5C7 can only be <2>
R8C3 can only be <2>
R2C2 can only be <7>
R4C3 can only be <4>
R2C1 can only be <4>
R4C6 can only be <2>
R5C6 can only be <4>
R6C5 can only be <5>
R5C2 can only be <6>
R6C1 can only be <2>
R4C5 can only be <8>
R4C9 can only be <7>
R4C1 can only be <5>
R5C9 can only be <8>
R5C8 can only be <5>
R4C2 can only be <3>
R5C1 can only be <7>
R4C8 can only be <6>
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