Jul 18 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 is the only square in row 6 that can be <5>
R8C2 is the only square in row 8 that can be <5>
R8C8 is the only square in row 8 that can be <8>
R9C3 is the only square in column 3 that can be <4>
R8C6 is the only square in column 6 that can be <1>
R8C1 can only be <7>
R1C7 is the only square in column 7 that can be <4>
Squares R3C6 and R4C6 in column 6 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 column.
R2C6 - removing <39> from <2349> leaving <24>
R6C6 - removing <39> from <369> leaving <6>
R5C3 is the only square in column 3 that can be <6>
Intersection of row 1 with block 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <2> from <2369> leaving <369>
R2C2 - removing <2> from <269> leaving <69>
Intersection of row 9 with block 9. The value <2> 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 <2> from <2479> leaving <479>
Intersection of column 9 with block 3. The values <15> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <1> from <139> leaving <39>
Squares R1C8<39>, R2C8<379> and R2C9<379> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C9 - removing <39> from <1359> leaving <15>
R3C9 - removing <39> from <1359> leaving <15>
Squares R1C5<358>, R3C4<389>, R3C5<358> and R3C6<39> in block 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <39> from <2349> leaving <24>
Intersection of block 2 with row 3. The value <9> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <9> from <1389> leaving <138>
Squares R2C4, R2C6, R7C4 and R7C6 form a Type-1 Unique Rectangle on <24>.
R7C4 - removing <24> from <247> leaving <7>
R7C5 can only be <6>
R7C1 can only be <9>
R9C5 can only be <3>
R8C4 can only be <4>
R7C9 can only be <4>
R7C6 can only be <2>
R8C9 can only be <3>
R2C4 can only be <2>
R2C6 can only be <4>
R5C5 is the only square in column 5 that can be <7>
R5C7 can only be <9>
R5C9 can only be <2>
R9C7 can only be <7>
R5C1 can only be <8>
R9C9 can only be <9>
R4C7 can only be <3>
R9C8 can only be <2>
R2C9 can only be <7>
R4C6 can only be <9>
R4C3 can only be <1>
R4C4 can only be <8>
R3C6 can only be <3>
R6C4 can only be <3>
R3C1 can only be <1>
R4C8 can only be <7>
R6C3 can only be <9>
R3C4 can only be <9>
R4C2 can only be <2>
R6C8 can only be <1>
R6C2 can only be <7>
R1C3 can only be <8>
R1C5 can only be <5>
R1C9 can only be <1>
R3C5 can only be <8>
R3C9 can only be <5>
R9C1 can only be <6>
R1C2 can only be <9>
R9C2 can only be <1>
R2C1 can only be <3>
R1C8 can only be <3>
R2C2 can only be <6>
R1C1 can only be <2>
R2C8 can only be <9>
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