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Maths EE - "Tetris" tiles


Because I couldn't manage to write a satisfactory EE on the topic I chose last year (it was too ambitious and I couldn't truly understand the theory behind it), now I have to completely change it and find something new. However, I need some help with defining the research question. I've encountered this problem that appeared on Polish Mathematical Olympiad and it sounds interesting:





"We can use tiles with the following shapes:


For every odd number n â‰¥ 7 determine the minimum number of tiles needed to form a square with a side length n.

We're allowed to turn the tiles, but they can't overlap."


And here come my questions: I know that finding the answer will not be enough, so what kind of generalization can I make about it? Or do you have any ideas for applying it to any other geometric shapes? Do you think it will work?

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