Aug 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <8>
R2C8 is the only square in row 2 that can be <6>
R3C1 is the only square in row 3 that can be <3>
R3C9 is the only square in row 3 that can be <5>
R1C2 is the only square in row 1 that can be <5>
R4C8 is the only square in row 4 that can be <7>
R4C6 is the only square in row 4 that can be <8>
R5C1 is the only square in row 5 that can be <6>
R6C2 is the only square in row 6 that can be <3>
R6C4 is the only square in row 6 that can be <6>
R7C2 is the only square in row 7 that can be <6>
R8C9 is the only square in row 8 that can be <3>
R8C8 is the only square in row 8 that can be <8>
R6C9 is the only square in row 6 that can be <8>
R7C5 is the only square in row 7 that can be <8>
R9C1 is the only square in row 9 that can be <5>
R9C7 is the only square in row 9 that can be <6>
R9C9 is the only square in row 9 that can be <7>
R7C4 is the only square in row 7 that can be <7>
Squares R7C6 and R9C6 in column 6 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.
R3C6 - removing <49> from <1249> leaving <12>
R6C6 - removing <9> from <129> leaving <12>
Squares R4C7 and R5C7 in block 6 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 block.
R5C9 - removing <24> from <1249> leaving <19>
R6C8 - removing <2> from <129> leaving <19>
R5C7 is the only square in row 5 that can be <4>
R4C7 can only be <2>
Squares R8C1 and R8C2 in block 7 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.
R7C1 - removing <4> from <249> leaving <29>
R9C2 - removing <4> from <249> leaving <29>
Intersection of block 2 with row 3. The value <2> 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.
R3C8 - removing <2> from <1249> leaving <149>
Intersection of block 4 with column 3. The value <2> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R1C3 - removing <2> from <129> leaving <19>
Intersection of row 1 with block 3. The value <2> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <2> from <129> leaving <19>
Squares R2C9 and R5C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <19> from <1249> leaving <24>
Squares R8C1, R8C2, R4C1 and R4C2 form a Type-2 Unique Rectangle on <14>.
R4C4 - removing <9> from <19> leaving <1>
R5C3 - removing <9> from <129> leaving <12>
R6C3 - removing <9> from <129> leaving <12>
R6C6 can only be <2>
R6C3 can only be <1>
R3C6 can only be <1>
R5C5 can only be <9>
R5C9 can only be <1>
R3C5 can only be <2>
R5C3 can only be <2>
R2C9 can only be <9>
R6C8 can only be <9>
R1C3 can only be <9>
R3C8 can only be <4>
R1C4 can only be <4>
R1C9 can only be <2>
R3C4 can only be <9>
R1C8 can only be <1>
R7C9 can only be <4>
R9C8 can only be <2>
R7C6 can only be <9>
R9C2 can only be <9>
R7C1 can only be <2>
R9C6 can only be <4>
R4C2 can only be <4>
R4C1 can only be <9>
R8C2 can only be <1>
R2C1 can only be <1>
R8C1 can only be <4>
R2C2 can only be <2>
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