Wave Function
(Published on 11. August 2023, 22:22 by shadow-nexus)
I have trapped a particle inside a sudoku grid that acts as an infinite potential well.
The wave function describing the particle's most probable positions does not change over time, allowing us to investigate its properties.
The wave fluctuates around row 5, in which the digits indicate the amplitude of the wave in their respective column (i.e., the number of digits belonging to the wave in that column).
Even though the wave tends to attract the lowest digits in each column, those digits must increase from both ends towards row 5. Digits outside the wave are unrestricted.
Prior experiments have already identified some local minima, but no concrete values so far.
Could you discover the numbers for the entire grid?
Rules
| Sudoku | Fill the grid with the digits 1-9 so that no row/column/3x3box contains repeated digits. |
|---|---|
| Entropic Line | Any set of three sequential cells along the entropic line in row 5 must contain a low digit (1,2,3), middle digit (4,5,6) and high digit (7,8,9). |
| Wave |
The grid contains a wave that the solver must locate.
In each column, the wave spans a contiguous run of cells, and must include the cell in row 5. Each digit in row 5 indicates for its column the number of digits belonging to the wave. Digits inside the wave must decrease as they move away from row 5 towards the (top and bottom) edge of the wave. |
| Local minima |
Less-than symbols "<" point to cells that each contain a digit that is smaller than their direct neighbours in the same column.
Cells separated by a white dot contain consecutive digits. Not all dots and not all less-than symbols are given (i.e., there are no negative constraints). |
| Example of a wave |
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The coloured cells belong to the wave, the uncoloured cells do not.
The different colours in this example show that the effect of each cell along the entropic line is limited to the corresponding column only. |
|---|
Solve online
Solution code: Row 1 and row 9 (no spaces)
Comments
on 13. August 2023, 03:01 by BenTen
There was some uncertainty at first but I managed to collapse the wave function in the end!
Really liked the theme of the puzzle and it was executed brilliantly. Well done.
on 12. August 2023, 12:47 by Elliott810
Brilliant construction! Thanks:)
