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How do I solve this "Lutz" sliding puzzle (by Dr. Volker Latussek)?

Goal:

Push the pieces one-by-one through the "door" into the frame and fit them all, without overlapping, and without using 3D moves.
Or equivalently, place all the pieces in the frame without overlapping, and try to remove them one-by-one through the "door", without using 3D moves.

5 by 5 square board. One edge has a slightly-less-than 3-wide gap; one side of this gap is a 2-wide wall and the other is a small but significant wall. The pieces are L, U, T, and Z pentominoes

There is no starting position, so the arrangement in the picture is just an example.

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I guess I found the solution.

My try

Getting out the T is really hard you have to turn it and play a little bit with it. In the picture it does not look clean but if you try it slowly it looks like it works. Anyways maybe my calculations of the puzzle are wrong. I am open for feedback.

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  • $\begingroup$ +1 Nice Puzzle ! +1 Nice Solution ! In your answer, you mention that moving T is hard and you have to tilt C too; In the last Image, it looks like that will be easier when you tilt and move the top L too. $\endgroup$
    – Prem
    Commented Sep 21, 2021 at 11:15

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