Jun 18 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <8>
R5C5 can only be <6>
R4C1 is the only square in row 4 that can be <5>
R5C2 is the only square in row 5 that can be <8>
R5C7 is the only square in row 5 that can be <2>
R4C7 can only be <6>
R4C2 is the only square in row 4 that can be <2>
R6C2 is the only square in row 6 that can be <6>
R8C8 is the only square in row 8 that can be <5>
R2C6 is the only square in row 2 that can be <5>
R1C7 is the only square in row 1 that can be <5>
R9C4 is the only square in row 9 that can be <2>
R9C6 is the only square in row 9 that can be <6>
R9C9 is the only square in row 9 that can be <8>
Intersection of row 8 with block 8. The values <49> 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.
R7C4 - removing <4> from <348> leaving <38>
R7C5 - removing <4> from <1347> leaving <137>
Intersection of row 9 with block 7. The value <3> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <3> from <134> leaving <14>
Squares R5C8<49>, R6C7<47> and R6C8<479> in block 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <479>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C9 - removing <47> from <1347> leaving <13>
Squares R4C3, R4C9, R6C3 and R6C9 form a Type-1 Unique Rectangle on <13>.
R6C3 - removing <13> from <1349> leaving <49>
Squares R5C3 and R6C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <9> from <179> leaving <17>
R9C3 - removing <4> from <347> leaving <37>
Squares R1C3 and R2C2 in block 1 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 block.
R1C1 - removing <1> from <189> leaving <89>
Squares R1C1 and R3C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C1 - removing <9> from <1349> leaving <134>
Squares R5C3 and R6C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C1 - removing <4> from <134> leaving <13>
Squares R5C3, R5C8, R6C3 and R6C8 form a Type-1 Unique Rectangle on <49>.
R6C8 - removing <49> from <479> leaving <7>
R6C7 can only be <4>
R2C8 can only be <4>
R2C4 can only be <3>
R5C8 can only be <9>
R5C3 can only be <4>
R6C3 can only be <9>
R9C7 can only be <7>
R9C3 can only be <3>
R7C9 can only be <4>
R7C4 can only be <8>
R7C1 can only be <1>
R9C1 can only be <4>
R4C3 can only be <1>
R4C9 can only be <3>
R1C3 can only be <7>
R6C1 can only be <3>
R6C9 can only be <1>
R7C6 can only be <7>
R8C2 can only be <7>
R7C5 can only be <3>
R2C2 can only be <1>
R1C9 can only be <6>
R1C4 can only be <9>
R3C9 can only be <7>
R2C5 can only be <7>
R3C5 can only be <4>
R8C5 can only be <1>
R8C6 can only be <9>
R8C4 can only be <4>
R3C6 can only be <8>
R1C1 can only be <8>
R3C4 can only be <6>
R3C1 can only be <9>
R1C6 can only be <1>
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