Dodecadoku
(Published on 21. November 2025, 12:34 by Video Floral)
Play online with SudokuPad
Rules:
- Fill the grid with the letters A to O so that no letter is repeated in a row, column, or box.
- Within each box, every cell is connected to five other cells (purple lines). Due to their distance, the connection between the upper left cell and the lower right cell in each box is marked by two open lines.
- Every cell has a secret friend in another box. These cell pairs point to each other by displaying the name of their friend's box with their letter. (Box names are marked in purple.)
- In their respective five-cell neighborhood, two befriended cells are always framed by an identical five-letter sequence. This five-letter sequence surrounds one of the two cells clockwise and the other cell counterclockwise. (See example below.)
Please note:
- Due to the large number of letters and the practical necessity of a keyboard, it is virtually impossible to solve the puzzle in the mobile version on a smartphone. I recommend to use a PC.
- Make sure to activate the Letter Tool in the settings.
- Sudoku Pad's solution timer does not stop automatically because it does not recognize letters as possible solutions. You can stop the timer manually when you have solved the puzzle. :)
Example:
- Cell Y in box X and cell X in box Y are considered befriended cells because they point to each other's respective boxes.
- They are therefore framed by an identical sequence of five letters. This sequence is arranged once clockwise and once counterclockwise around the two befriended cells.
- One possible conclusion from the given example would be that box Q must contain the letters P, R, X, and Y. (This is because each cell needs a secret friend in another box, and cell Q in box Y must therefore have a counterpart Y in box Q. Three of the neighbors of this cell pair (P, X, R) are already known and must therefore also be found in box Q.)
Solution code: All 12 letters in Box L (uppercase). One row after another, from left to right. No spaces.
Comments
on 21. November 2025, 12:44 by Video Floral
I'm not sure how interesting this is, but there is actually a little backstory to this sudoku. Originally, I didn't really intend to create a new puzzle. I simply wanted to study dodecahedrons and their geometric arrangement possibilities in quasi-periodic structures. (This topic has been on my mind for a few years now.) And at some point during my exploration process (I don't want to call it research, as it's not really scientific), I wondered what would happen if, instead of changing the objects and their composition in space, you would change the nature of the space itself. What would happen, for example, if you placed a collection of dodecahedrons in a non-euclidean space with spherical geometry? Would it be possible to completely fill such a space if each face of one dodecahedron connected directly to the face of another one? And how many dodecahedrons would be required, at a minimum, to form a perfect, self-enclosed pattern?
I experimented with SketchUp for a while, but couldn't find a solution. However, because the question kept nagging at me, I finally programmed an algorithm that systematically tried out all possible compositions for different numbers of dodecahedrons in spaces with spherical geometry. It took about two weeks to complete the algorithm. (The calculation time was then 1.6 seconds.) The result: you need at least 15 dodecahedrons. (Incidentally, if my algorithm didn't make any mistakes, it's not possible to build such a self-enclosed pattern with 16, 17, 18, 19, or 20 dodecahedrons. I didn't continue searching. Obviously, the computing time increased exponentially with each additional object, and I was already thrilled with the elegance of the pattern I had found.)
For a while, it just sat on my computer as a simple table. But I wanted to do something with it. Eventually, I thought I could try to use the pattern within a sudoku. But oh boy, was that difficult. I'd rather not say how long it took me to come up with a functioning sudoku grid. But finally – I had to cheat a little with three boxes and move some cells into a separate column – it somehow worked. Until the very end, I wasn't sure whether this dodecahedron mechanism would even be suitable for an interesting puzzle. Ultimately, however, I think it works pretty well. In fact, I had to be careful that the clues didn't lead to an avalanche of conclusions too quickly, which I perhaps didn't entirely succeed in doing. For me, the beginning of the puzzle is much more exciting than the relatively intuitive end. But maybe that's the case with most sudokus...
Anyway, that's the story behind this strange looking puzzle. After all this work and in light of everything I've learned in the process, I'm really excited to finally share it with you.
Have a great weekend!
Video Floral
