This stuff was completely new to me. And it was the hardest task for me in 12/2025 so far. But I learned a lot. Also about continued fractions. It is amazing what others already discovered hundreds of years ago.

One Idea has maybe a chance under certain circumstances. You calculate the density ( tiles to set / area) and by constructing you try to keep the density consistent over the construction steps. This reduces the search space a lot.

Also a good approach is the tetris approach: bsky.app/profile/fran...

I wasted 2 days in bin packing research before I saw the same solution like you. But I think some ideas I've found aren't bad. For instance what about looking for pairs of packed shapes and an appropriate estimation of the density and then trying to combine the packed shapes further recursively.

... And allowed me to find the minimum allowed SUM.

That worked. But the interesting part was: I was able to use the precalculated SUM - range from clpfd to find the lowest number where a Z3 calculation was no longer unsat. Even when clpfd was not able to complete the formula as a whole it was able to restrict the allowed range of the SUM variable.

Then I thought I switch to a solver in Swi Prolog : clpfd. The example data were processed even faster but only some of the input data I was able to process. Some were just too slow. After a while I decided to connect via the janus library from prolog to python and use Z3 there.

I solved the task of day 8 in prolog and after that I wrote the start data and some data during the calculation in separate files which I then read into an R program. The visualization in R is made with the rgl library. Thanks for the kudos.