I found:

• Family Relations, which tests another set of relations,
• Your family tree, which seems to be a (significant) superset of this problem?

Wow, you were on this fast!
This idea came from this riddle my Dad liked to say when I was a kid. I hadn't seen anything strictly similar to it, but I'd love to check out the other one if you find it.
This is my first kata submition so I'm not quite used to the process. Thanks for trying it out!

I didn't indend it to be hard optimization Kata so if your solution can pass large random tests I would like for it to also pass all other tests.

Ooops! I have just learned that 12s limit is for all tests groups cumulative and not per test group so accidentally I made it much harder to pass than I thought!
I thought I give roughly 4x overhead over my naive solution, while it was less than 2x.

The tests have been modified:

• fixed tests are very small part of all tests now, and their order is now shuffled to avoid simple trick like yours.
• random tests have been split into 3 groups with approximately even performance within the group (medium size board, large board with short solutions and large board with long solutions).

done

Do you think I should include a link to a website that shows this? Or, more radically, I could provide code that does this - would make the kata more accessible.

I do not know. Did you make a point to check for one prior to submitting your kata to beta?

Yes, I got that part. But which one is it a duplicate of?

That there already exists a kata mostly or completely like this.

Hello. Sorry, a duplicate of what?

To be fair, I did write the Road class, so of course I know how it works. I imagine that figuring out what it does and how you can use it raises this kata to a 6kyu. I think that it is a fair rating :)

I voted high because I think that a task where users have to control the execution, instead of just accepting inputs and reacting to values, has another layer of difficulty.

Frankly, I've no idea. Some of my friends have been unable to do it but I still believe its a 7.

I put the smaller random tests into individual it blocks, but left the big ones together in a single it block.

Added (finally)

I made some adjustments based on your feedback. I hope with the adjustments I made to the feedback that it's more clear what I want people to try and do. I also changed the title to this Kata to reflect this clarity.