A housewife is waiting for guests and havehas prepared a cake. She doesn't know how many guests will come, but it will be $n-1$, $n$, or $n+1$. What is the minimal number $f(n)$ of pieces the cake should be cut to make it possible to divide between guests equally?
For $n=2$, $f(n)=f(2)=4$:
The problem was posed 16.10.2018 by Oleksandr Maksymets on page 76 of Volume 2 of the Lviv Scottish Book.
The prize: Cooked duck or lunch + beer!