That's Exciting!
(Published on 4. August 2025, 16:27 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. A cell with an arrow is a “photon” with “energy” E given by the digit in the cell. The immediately neighboring cell pointed at by the arrow is the “lower state” of an “associated quantum system”. An associated quantum system is a pair of cells within one column that consists of a lower state, pointed at by a neighboring photon, and an upper state somewhere above the lower state. The “energies” L and U of the lower and upper states, respectively, are given by the entered digits. Each photon excites its associated quantum system; this means that the energy of the upper state is given by the sum of the energy of the lower state and the energy of the photon, i.e., U = L+E. In addition, the upper state must be located E cells above the lower state. A cell may act as several lower and/or upper states associated with different photons.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: This puzzle simulates the resonant absorption of a photon by a quantum system. According to the principle of energy conservation, the energy of the upper state must be equal to the energy of the lower state plus the photon energy. The photon energy is E = hf, where f is the frequency of the photon and h is Planck's constant. In an energy diagram, the distances between the states involved are usually drawn so that they are proportional to the energy difference, as in the puzzle.
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad. The yellow cell in column 1 is a photon with energy 1 exciting the quantum system marked in yellow in column 2. The two photons in column 4 marked in blue and green excite two associated quantum systems in column 3 marked with corresponding colors. Note that the upper state is shared by the latter two quantum systems.
Solution code: All digits of row 1 (from left to right) followed by column 5 (from top to bottom) without spaces.
Comments
on 10. August 2025, 10:16 by zoonel
really nice rule, I like it a lot!
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Great, thank you! - TB
on 9. August 2025, 10:15 by zrbakhtiar
Wow. This is easy and approachable. For solvers, don't be scared by long rules. Take your time and look at the example. Nice puzzle.
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Glad that you enjoyed it! - TB
on 8. August 2025, 09:17 by MartinR
Once the rules are understood, does flow quite well.
However on that point, I think it would be useful to have a simplified summary of the rules as well as the thematic one.
While a theme may be good, it can also be confusing - almost didn't give this a go based on the rules being one long paragraph
(maybe something like,a digit X in a cell pointed to by an Arrow has the digit X+N in the cell N rows above it, where N is the value in the arrowed cell)
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Thanks for playing and suggesting a simplified version of the rules. This puzzle is part of a series designed to employ Sudoku for physics teaching and science outreach activities (see also my other puzzles). Thus the specific wording. But I will keep in mind the idea of adding simplified rules. On some of my Sudokus, I have in fact separated the physics-themed background from the actual rules, while on other occasions I felt it made more sense to combine everything into one piece of text. - TB
on 5. August 2025, 22:09 by cozmic72
Got worried when I only had ground states near the bottom of the grid left, but was happy to discover that the band gap wasn’t off the charts. A fairly easy solve once you get the hang of the rules.
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Many thanks for playing and commenting! - TB
on 4. August 2025, 22:20 by NotSoMagnifique
Wonderful and quite breezy once I got the hang of it!
I'm now thinking of implications of these photon arrows with other common variants...
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Thanks a lot, glad you liked it! - TB
