This Kropki Pairs Sudoku by Philip Newman has an amazing arrangement of numbers and dots, both visually and logically.

PDF

or solve online (using SudokuPad)

Theme: Tilting Kropmills

Author/Opus: This is the 9th 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 white circle is given between two adjacent cells, then the two numbers in those cells must differ by 1. 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 (🎩🥳): 8:00; One party hat (🥳): 15:00. All other solvers earn a 🦕: Speckled Sousatitan.

Thomas Hits the GAS (highlight to view): 3:51, 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 and solving video with explanation from GAS team.

Note: Follow this link for more Genuinely Approachable Sudoku puzzles on this site. 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.