#A38: Kropki Pairs

 As someone who likes to set puzzles a few clues at a time, Kropki Pairs feels more natural to set than classic Kropki because of the constraint it removes. However, this comes at the cost of making the logic a bit more straightforward, or the added benefit of being more streamlined, depending on how you look at it.

Rules: Place a number between 1 and the grid width into every cell such that numbers never repeat in any row or column. Cells separated by a white dot contain numbers that differ by one. Cells separated by a black dot contain numbers that have a ratio of 2:1.

penpa link

penpa link

(This post was previously retracted for maintenance on 4/27/26 and reuploaded on 5/7/26)