Thanks for raising this issue. It should be fixed now.

In python, all tests after size 12 pass.
I've tried passing [[]] and [[1]] and both pass the tests

If you try and solve the whole puzzle at once with A*, it will be too slow. As Blind4Basics said below, you cannot just search for the answer.

Your algorithm has to solve the puzzle instead of just searching (if that makes sense). However, although you can't purely use A* to search for the solution, it can greatly help you a lot to do parts of the puzzle depending on your implementation.

Also, one thing to note is that is you don't have to return the shortest solution. :)

Description is very unclear... I'm having a go in python, I don't even know where I'm supposed to return an action to make a guess

I approached this problem with A* and I can solve 3x3 puzzles.
Yet, when I start a 4x4, my solution always timesout.
My heuristic is the sum of the distance between each cell's current place and it's objective place.

Has anyone used the same approach with the same or different heuristic and finished the problem?

you can do the jump A->C only if B is already used. Otherwise you'd do A->B->C

If I wanted to cross from A to C, A -> C, without B being already selected, would that be possible, or would that translate into A -> B, B -> C?

Not an issue.

This kata spoils game of thrones :(