Jun 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <4>
R2C5 is the only square in row 2 that can be <6>
R2C9 is the only square in row 2 that can be <7>
R1C5 is the only square in row 1 that can be <7>
R1C6 is the only square in row 1 that can be <9>
R3C6 can only be <5>
R6C6 can only be <2>
R4C6 can only be <1>
R4C5 can only be <8>
R6C5 can only be <9>
R5C5 can only be <5>
R1C9 is the only square in row 1 that can be <5>
R3C7 is the only square in row 3 that can be <9>
R5C2 is the only square in row 5 that can be <9>
R6C4 is the only square in row 6 that can be <7>
R4C4 can only be <6>
R4C1 is the only square in row 4 that can be <7>
R6C8 is the only square in row 6 that can be <6>
R5C1 is the only square in row 5 that can be <6>
R6C9 is the only square in row 6 that can be <8>
R9C2 is the only square in row 9 that can be <6>
R8C2 is the only square in column 2 that can be <8>
R9C9 is the only square in column 9 that can be <3>
Squares R5C8 and R5C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C7 - removing <2> from <234> leaving <34>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <3> from <123> leaving <12>
R9C7 - removing <4> from <124> leaving <12>
Intersection of column 1 with block 7. The values <45> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C3 - removing <4> from <1249> leaving <129>
R8C3 - removing <4> from <12349> leaving <1239>
Squares R6C3, R6C7, R4C3 and R4C7 form a Type-1 Unique Rectangle on <34>.
R4C3 - removing <34> from <234> leaving <2>
R4C2 can only be <3>
R4C7 can only be <4>
R6C3 can only be <4>
R6C7 can only be <3>
R2C8 is the only square in row 2 that can be <3>
Squares R7C2 and R9C7 form a remote naked pair. <12> can be removed from any square that is common to their groups.
R9C1 - removing <2> from <245> leaving <45>
R7C9 - removing <12> from <124> leaving <4>
R3C9 can only be <2>
R3C1 can only be <8>
R5C9 can only be <1>
R2C7 can only be <1>
R5C8 can only be <2>
R2C2 can only be <2>
R9C7 can only be <2>
R1C8 can only be <8>
R3C8 can only be <4>
R1C1 can only be <3>
R8C8 can only be <1>
R8C4 can only be <9>
R9C5 can only be <4>
R1C3 can only be <1>
R7C3 can only be <9>
R7C2 can only be <1>
R7C4 can only be <5>
R8C3 can only be <3>
R7C1 can only be <2>
R9C4 can only be <1>
R9C1 can only be <5>
R8C5 can only be <2>
R8C1 can only be <4>
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