Right, that's why I'm not posting this as an answer to the stack exchange question. Though I'm pointing out that it's not necessary to remove any pieces, and also suggesting that there may be an interesting math problem still there in this case.
I guess the obvious question is "given x amount of slack per piece, after how many pieces can I fit in on piece the wrong way without tension", but that feels more like an engineering problem than a math puzzle.
In this case not-so-brute force of fitting actual pieces, since it won't take that many. And otherwise estimates based on highly simplified approximations.
