Hooke's Law
(Published on 18. July 2025, 15:00 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. Each cage represents a weight and each red line an elastic spring. The upper end of each spring is fixed in space to the black dot. A weight applies a downward force to the spring above it to which it is connected. This force is equal to the sum of the digits in the weight. Digits must not repeat within a weight. The extension of each spring shown in the puzzle follows Hooke's Law: The number of cells of the spring is equal to the applied force divided by the spring constant. The spring constant is given by the sum of the digits on the spring. Each connected pair of spring and weight is treated independently of the other pairs: Assume that any given pair does not influence any other pair even if they are located in neighboring cells, i.e., springs are not connected to weights above them.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: Hooke's law describes the compression or extension of a spring with respect to its equilibrium position as being linearly proportional to the applied force, just as stated in the puzzle rules. This empirical connection was found by Robert Hooke already in 1676. While it is only an approximation, it nevertheless works well if the extension is not too large.
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad.
Solution code: All digits of row 2 (from left to right) followed by column 7 (from top to bottom) without spaces.
Comments
on 17. August 2025, 17:53 by Firebird
Happy to see some puzzles by you again! This one was really nice, lots of exciting deductions.
----------
Great to see you solve some again… Thank you for commenting. - TB
on 21. July 2025, 20:20 by PhysicistFromFunen
What a compelling ruleset ;) Lovely setting as well - The break in was not where I expected at first glance, and the key digit was even more of a surprise
----------
Thank you so much for playing and commenting! - If you like physics-based Sudokus, feel free to check out my other puzzles; there are quite a few more. - TB
on 19. July 2025, 14:28 by RockyRoer
You Hooked me! Nice exercise in sums and products! Thanks for the puzzle!
----------
Nice pun! Thanks a lot for playing and commenting. - TB
on 19. July 2025, 10:26 by Tobias Brixner
Added 4x4 example
on 19. July 2025, 01:23 by Kazeyoubi
It is really amazing to apply Hooke's Law here. Great puzzle!
on 18. July 2025, 20:31 by trashghost
Some very fun and interesting deductions with this rule set! Thanks for the puzzle!
----------
Thank you, glad you liked it! - TB
