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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?

Idk I think the puzzle may generate in an unsolvable way? Twice now I have solved the puzzle down the the last 3 tiles (plus empty space) in the bottom corner 2x2 (tiles 11, 12, 15) and they are juxtaposed in a way that can't be fixed.