In the super nintendo game "Lufia II", game developers included multiple little block puzzles throughout the game. However, one in particular is considered a standout:
This is a kind of sliding puzzle similar to the "15 puzzle" (https://en.wikipedia.org/wiki/15_puzzle). Here, your goal is to bring the biggest block (the one with the treasures) all the way to the lower middle of the space (so your character can access them).
What I was wondering was not the solution itself, but more: how does one create a problem like this? I mean, it doesn't seem trivial at first glance if there is or not a solution to some particular configuration (specially one with uneven shapes). Is there some kind of mathematical area that is suited to analyse if, given some set of shapes, initial configuration and goal, a sliding block puzzle has a solution?
Or maybe even going a step further: is there some analytical way that could help one construct these kind of problems with different "difficulties" (in some well-defined way)?
==== Edit: after posting the question, i found out that this is not an original puzzle - this example is called Klotski (https://en.wikipedia.org/wiki/Klotski). Nevertheless, i guess the question still stands.