Sep 19 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R2C8 is the only square in row 2 that can be <2>

R2C1 is the only square in row 2 that can be <3>

R3C5 is the only square in row 3 that can be <1>

R7C5 is the only square in row 7 that can be <3>

R6C4 is the only square in row 6 that can be <3>

R5C7 is the only square in row 5 that can be <3>

R8C3 is the only square in row 8 that can be <3>

R7C1 is the only square in column 1 that can be <8>

R8C5 is the only square in column 5 that can be <7>

R8C2 can only be <5>

R7C2 can only be <7>

R9C3 can only be <1>

R9C6 can only be <8>

R6C3 can only be <2>

R9C4 can only be <5>

R5C2 can only be <6>

R9C9 can only be <6>

R9C7 can only be <7>

R3C2 can only be <2>

R3C1 is the only square in row 3 that can be <6>

R7C7 is the only square in column 7 that can be <1>

R7C6 can only be <9>

R8C9 can only be <9>

R8C6 can only be <1>

Squares R3C9 and R7C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R4C9 - removing <4> from <24> leaving <2>

R5C9 - removing <4> from <1248> leaving <128>

R5C6 is the only square in row 5 that can be <2>

Intersection of row 1 with block 1. The value <5> 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.

R3C3 - removing <5> from <457> leaving <47>

Intersection of column 5 with block 5. The values <59> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.

R5C4 - removing <9> from <489> leaving <48>

Squares R2C4 and R5C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C4 - removing <4> from <479> leaving <79>

R3C4 - removing <4> from <479> leaving <79>

Squares R7C8, R7C9, R3C8 and R3C9 form a Type-1 Unique Rectangle on <45>.

R3C8 - removing <45> from <459> leaving <9>

R3C4 can only be <7>

R5C8 can only be <4>

R5C4 can only be <8>

R7C8 can only be <5>

R4C7 can only be <9>

R7C9 can only be <4>

R3C9 can only be <5>

R3C3 can only be <4>

R1C4 can only be <9>

R4C1 can only be <5>

R5C9 can only be <1>

R2C4 can only be <4>

R6C5 can only be <9>

R6C9 can only be <8>

R6C1 can only be <1>

R5C5 can only be <5>

R2C7 can only be <6>

R1C6 can only be <6>

R2C5 can only be <8>

R1C7 can only be <4>

R4C5 can only be <6>

R1C1 can only be <7>

R5C3 can only be <7>

R4C6 can only be <4>

R5C1 can only be <9>

R1C3 can only be <5>

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