I'm pretty confident with the process to solve slider puzzles, but I think the first one with the teacher might generate in an unsolvable way. I solved the top 2 rows and the 2 columns to the left, leaving me the final 2x2 grid with the empty space, and it is not solvable from there. I don't think this should happen AFAIK with a solvable slider puzzle. Are the pieces randomized and could it be possible that the puzzle breaks sometimes?