Moving in Circles
(Published on 19. October 2025, 15:00 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. A cage represents an object whose mass, m, is given by the clue in the top left corner. If the clue contains a slash, the mass is given in fractional notation (e.g., m = 1/3 means a mass of one third). Each object moves with a velocity, v, given by the digit in the cage, on a circular trajectory around exactly one circled cell that is displaced by r cells either horizontally or vertically from the cage. The circled cell contains as a digit the centripetal force, F = m v2 / r, required to maintain the circular motion of the associated object. The circular trajectory need not be contained fully within the Sudoku grid.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: The puzzle implements the correct physical equation for the Centripetal force that makes an object with mass m follow a curved path. In this puzzle, the path is assumed to be circular as a special case.
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad. The large colored circles indicate the circular motion of the objects around their associated force centers in matching colors.
Solution code: All digits of row 2 (from left to right) followed by column 8 (from top to bottom) without spaces.
Comments
on 22. October 2025, 00:08 by dzamie
This one was easier than the gravity one, with a couple of basically free pairs. Very cool, though, and I'm glad that every pair shared a row or column; it would've been quite tricky to worry about, say, r4c5 and r8c8 being paired with values of 5 each (5 = 1 * 5^2 / sqrt(3^2 + 4^2)).
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Thanks a lot. So glad you liked it! - TB
on 21. October 2025, 22:03 by Felis_Timon
Can multiple cages share a circle (then potentially leaving other circles unused)? I think I can guess what the answer to my question is gonna be but I'd rather ask anyway
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Each circle has exactly one circling cage. I meant to state that with „exactly“ in the rules but realize from your question that I may have not expressed that without ambiguity. - TB
on 19. October 2025, 18:29 by OutOfMyMindBRB
Very nice puzzle with interesting logic - thanks :-)
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Many thanks for playing and commenting! - TB
