This is a post about axles, a game I put together with help from Gemini. This post might make more sense if you go play a round before you read it.

Background

In 2024, I saw a post on the twisty puzzles forum about the Peterhoff-Smolensk puzzle. I thought it was a really nice idea, and filed it on my mental “I should think more about this” list.

Simulator in Rust

I didn’t know what specifically I wanted to do, just that I wanted to do something. My two main ideas were to make 3d printed version of it, and to make some kind of interactive digital version of it. I decided to start with something in between - an analysis tool to help me figure out what sort of puzzles I wanted to make.

As an experiment, I asked Gemini to write the first version of this simulator in Rust (but on a square grid instead of a hex grid). The results were better than I expected! With minimal edits, I was able to input a hardcoded goal configuration, and then run the code to answer questions like “what start is furthest from the goal state?”

I modified the code to try random 3x3 starting configuration and print cases where the furthest node was especially far away. The results were impressive, the AI generated code found cases like this one, where these two states were 36 moves apart.

Goal:
|↑ ^><|  |↑ >v|  |↑ |
|↑ ^>v|  |↑ v|  |↑ ^>|
|↑ ><|  |↑ >|  |↑ ^|

Start:
|↑ ^><|  |↑ >v|  |→ |
|← ^><|  |↑ v|  |↑ ^>|
|→ ^v|  |↑ >|  |↑ ^|

Interactive Simulator

I cut out some scraps of paper to try to play with this puzzle, but found it a little annoying to keep everything aligned, so I turned to Gemini again, and asked if it could make the code interactive.

I was expecting some sort of stdin/stdout interface, where I could give moves to the rust code one at a time. To my surprise, Gemini rewrote the simulator in javascript, and opened an interactive gui where I should interact with the js that it wrote. Parts of it were a little clunky, but it crystallized my goals in my head. I wanted to polish this javascript version to make it easy for others to play with these puzzles.

GUI stuff

Polishing the gui wasn’t that hard. The AI had done a lot of the bits that I’m inexperienced with (css, event handling…), and I just had to edit them to work the way I wanted. Where possible, I did this using more AI prompting; though there were a few cases where the AI did quite a bad job and I ended up reverting its changes and making them manually.

It got fixated on drawing the dots on each cell using css pseudo-elements, and I’m not sure that approach is viable at all.

Puzzle generation

When generating the goal state, it’s undesirable if there’s a loop of blockages, such that A blocks B blocks C blocks D blocks A. When this happens, none of those axles can turn, which means that much of the puzzle isn’t intractable.

To prevent this problem, I came up with the following:

assign each axle a random and unique id between 1 and num_axles
(treat out-of-bounds as having some arbitrary id, like num_axles/4)

for every position where it's possible to place a dot:
    if a lower id would block a higher id - do nothing
    if a higher id would block a lower id, add a dot with X% probability.
    if any axle has all four blockers, that's boring, remove one blocker.

I’m quite pleased with this approach. It is computationally cheap, and scales linearly with the number of axles; and it’s easy to convince myself that this never generates those undesirable loops of blockers.

Additional modes

Once I had that working, I decided to add some additional modes. By tweaking the probability with which blockers are generated, I could make an “easy” mode with sparser boards. And then I added support for diagonal blockers, and called that “Hard” mode.

Closing thoughts

My favorite part of this project is the speed and output of puzzle generation. The quality of puzzles is good enough that I don’t feel the need to add human-authored ones.

I’m also quite happy with the usability. I watched a few friends trying it out, and they seemed to find the GUI intuitive, in a way that let them engage with the puzzle’s rules.

This was my first time using AI in this way and I found the experience fascinating. It was quite good at some things, but also got hopeless stuck on others. I think the best part was the speed with which it got me something I could interact with. That helped me refine my goal, and saved me a few hours.

Future work

The author of Peterhoff-Smolensk recently published a 3D version of their idea, which they call the Bomzh Cube

I think this idea is fascinating as well, and that it would be neat to have a digital simulator for it. I would need to learn quite a lot (or lean even harder into AI-assisted programming).