(This post is part of the Genuinely Approachable Sudoku (GAS) series.)
Some see the world in black and white. In this puzzle, the Faded Kropki dots don’t even have two colors, and come in white and white.

PDF

or solve online (using SudokuPad)

Author/Opus: This is the 14th puzzle from Bill Murphy, 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 circle is given between two adjacent cells, then it either means that (A) the two numbers in those cells must differ by 1, or (B) 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 (🎩🥳): 7:30; One party hat (🥳): 14:00. All other solvers earn a 🦕: Washed Out Wellnhoferia.

Thomas Hits the GAS (highlight to view): 3:05, 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.