Combinatorios and pyramids

Discussion in 'Advanced Applied Math' started by Loulou, May 2, 2022.

  1. Loulou

    Loulou

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    Hello everybody,
    I am trying to solve this problem but I need help:
    Suppose you have a pyramid (built with logs for example). You can only add a log if there are already two logs underneath and each new floor of the pyramid has one less log than the one before. The question is: for a pyramid with n logs on the first floor ( and n-1 logs on the second floor etc), on how many orders can the pyramid be built? n can be any natural numbers.
    For instance, if the base of the pyramid is 2, you can only build it in 2 ways. For the first log, you have the choice between two places on the first floor, then the second one has to be the other one on the first floor, and the third one has to be the only one on the second floor and that's it.
    Thank you very much, I can't solve it for n.
     
    Loulou, May 2, 2022
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