(This post is part of the Genuinely Approachable Sudoku (GAS) series.)
The title of today’s puzzle is a reference to the variant, yes; one number of each Ratio Pair must be half of the other. It’s also a reference to something else! (And the dots make a pattern that evokes cell division…)

PDF

or solve online (using SudokuPad)

Author/Opus: This is the 82nd puzzle from Philip Newman, part of the Genuinely Approachable Sudoku (GAS) team.

Rules: Standard Sudoku rules (insert a number from 1 to 9 into each cell so that no number repeats in any row, column, or bold region). If a black circle is given between two adjacent cells, then the two numbers must have a ratio of 2. Pairs of cells without circles can have any relationship.

GAS Time Standards (highlight to view): Two party hats (🎩🥳): 6:30; One party hat (🥳): 13:00. All other solvers earn a 🦕: Oops-I-Used-It-Again Opisthocoelicaudiinae.

Thomas Hits the GAS (highlight to view): 3:52, with SudokuPad replay file shared as a download for now (requires loading via settings menu with improvements expected before people should use this regularly).

Solution: PDF; solving video with explanation to be added later from GAS team.

Note: Follow this link for other less common variations of Sudoku.

Note 2: Comments on the blog are great! For a more interactive discussion, please also consider using our Daily GAS discussion post on the GMPuzzles Discord. Not a member of the Discord? Click this link for basic access.