May 30 - Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R1C6 is the only square in row 1 that can be <2>

R5C6 can only be <8>

R3C1 is the only square in row 3 that can be <4>

R2C9 is the only square in row 2 that can be <4>

R3C7 is the only square in row 3 that can be <5>

R2C1 is the only square in row 2 that can be <5>

R4C6 is the only square in row 4 that can be <4>

R4C2 is the only square in row 4 that can be <8>

R9C2 can only be <6>

R9C1 can only be <8>

R9C3 can only be <4>

R4C5 is the only square in row 4 that can be <9>

R4C9 is the only square in row 4 that can be <2>

R5C9 can only be <1>

R6C8 is the only square in row 6 that can be <5>

R7C4 is the only square in row 7 that can be <4>

R7C5 is the only square in row 7 that can be <2>

R9C9 is the only square in row 9 that can be <5>

R8C6 is the only square in row 8 that can be <5>

R3C6 is the only square in column 6 that can be <7>

R3C5 can only be <8>

R8C4 is the only square in row 8 that can be <8>

Squares R8C5 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R8C7 - removing <7> from <137> leaving <13>

Squares R5C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R6C1 - removing <23> from <2369> leaving <69>

Intersection of row 1 with block 1. The value <6> 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.

R2C3 - removing <6> from <168> leaving <18>

Squares R2C3 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R2C4 - removing <1> from <139> leaving <39>

R3C4 is the only square in column 4 that can be <1>

R3C2 can only be <9>

R6C2 can only be <2>

R1C1 can only be <6>

R8C2 can only be <1>

R5C1 can only be <3>

R8C7 can only be <3>

R7C3 can only be <3>

R8C1 can only be <2>

R4C7 can only be <7>

R7C8 can only be <1>

R6C1 can only be <9>

R4C8 can only be <3>

R9C7 can only be <9>

R5C4 can only be <2>

R6C3 can only be <6>

R2C8 can only be <8>

R9C4 can only be <7>

R1C7 can only be <1>

R7C9 can only be <6>

R1C3 can only be <8>

R2C3 can only be <1>

R1C8 can only be <7>

R7C6 can only be <9>

R8C9 can only be <7>

R8C5 can only be <6>

R1C9 can only be <9>

R6C4 can only be <3>

R6C5 can only be <7>

R2C4 can only be <9>

R2C6 can only be <6>

R2C5 can only be <3>

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