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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