Jul 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <5>
R8C5 is the only square in row 8 that can be <5>
R8C7 is the only square in row 8 that can be <7>
R4C7 can only be <2>
R8C4 is the only square in row 8 that can be <3>
R2C5 is the only square in row 2 that can be <3>
Squares R5C4 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C1 - removing <4> from <2349> leaving <239>
R5C2 - removing <4> from <3479> leaving <379>
R5C3 - removing <4> from <24569> leaving <2569>
R5C5 - removing <14> from <12468> leaving <268>
Squares R5C4 and R5C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <4> from <46> leaving <6>
Intersection of block 8 with column 5. The value <1> only appears in one or more of squares R7C5, R8C5 and R9C5 of block 8. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R1C5 - removing <1> from <1479> leaving <479>
R3C5 - removing <1> from <1479> leaving <479>
R3C2 is the only square in row 3 that can be <1>
R1C7 is the only square in row 1 that can be <1>
R7C5 is the only square in row 7 that can be <1>
R9C3 is the only square in row 9 that can be <1>
R9C1 is the only square in row 9 that can be <2>
Squares R5C1 and R6C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C2 - removing <39> from <379> leaving <7>
R5C3 - removing <9> from <2569> leaving <256>
R6C3 - removing <9> from <269> leaving <26>
R4C2 can only be <4>
R4C3 can only be <5>
R4C8 can only be <7>
R5C8 is the only square in row 5 that can be <5>
Intersection of row 9 with block 9. The value <3> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C9 - removing <3> from <369> leaving <69>
Squares R5C4, R5C6, R2C4 and R2C6 form a Type-1 Unique Rectangle on <14>.
R2C6 - removing <14> from <149> leaving <9>
R8C6 can only be <4>
R8C3 can only be <9>
R5C6 can only be <1>
R9C5 can only be <9>
R9C9 can only be <3>
R9C7 can only be <4>
R5C4 can only be <4>
R7C2 can only be <3>
R2C7 can only be <8>
R2C3 can only be <4>
R2C4 can only be <1>
R7C1 can only be <4>
R6C2 can only be <9>
R1C3 can only be <8>
R1C1 can only be <9>
R6C7 can only be <3>
R6C8 can only be <6>
R5C1 can only be <3>
R5C7 can only be <9>
R6C3 can only be <2>
R7C8 can only be <9>
R7C9 can only be <6>
R3C8 can only be <4>
R1C9 can only be <7>
R1C5 can only be <4>
R3C9 can only be <9>
R3C5 can only be <7>
R5C9 can only be <8>
R5C5 can only be <2>
R6C5 can only be <8>
R5C3 can only be <6>
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