Laser Cavities
(Published on 28. October 2025, 16:25 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. A horizontal (vertical) red line across the width of one cell represents a horizontal (vertical) mirror. Each pair of horizontal mirrors displaced vertically by L cells and each pair of vertical mirrors displaced horizontally by L cells forms a laser cavity of length L. For each cavity, the product of the digits in the two mirror cells must be twice the cavity length. If a cell contains both a horizontal and a vertical mirror, its digit must be valid for both associated cavities.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: The electric field of a laser forms a standing wave in its cavity with nodes on the mirrors. Thus, a cavity always contains integer multiples (m) of half a wavelength (λ) along its length (L), i.e., L = mλ/2. Rearranging, we have 2L = mλ. If we require m to be written on one mirror of the cavity and λ on the other, this leads to the puzzle rules.
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad. The three cavities are highlighted with different colors.
Solution code: All digits of column 4 (from top to bottom) without spaces.
Comments
on 29. October 2025, 10:41 by Scorps
Think it took me longer to read the rules than finish the puzzle :D but a very nice idea and I enjoyed it
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Glad you enjoyed it, thanks for playing! - TB
on 28. October 2025, 20:47 by dzamie
This one was really easy. Sort of like a simpler version of your gravitational force puzzle. Though I suppose there's not really much you can do with L = mλ/2 as far as intricacy of calculation.
Still, fun little snack of a sudoku!
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Many thanks for playing and commenting! Indeed, this is the simplest Sudoku I have set so far. Maybe interesting as a starting point for more intricate ones. - TB
on 28. October 2025, 18:02 by CitrusGremlin
Fun puzzle! I hope this rule set can support meatier puzzles because I found it very fun.
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Glad you liked it, and thanks for commenting! I might think of a follow-up. As of now, there are several other physics-themed puzzles with varying degrees of difficulty. - TB
on 28. October 2025, 16:41 by Tobias Brixner
Updated SudokuPad link such that formulation of rules is consistent (no change in logic).
