>A housewife is waiting for guests and have 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 $n=2$, $f(n)=f(2)=4$:


[![enter image description here][1]][1]

The problem was posed 16.10.2018 by Oleksandr Maksymets on page [76][2] of [Volume 2][3] of the [Lviv Scottish Book][4].

**The prize:** Cooked duck or lunch + beer!


  [1]: https://i.sstatic.net/drVRL.jpg
  [2]: http://www.math.lviv.ua/szkocka/viewpage.php?vol=2&page=76
  [3]: http://www.math.lviv.ua/szkocka/viewbook.php?vol=2
  [4]: http://www.math.lviv.ua/szkocka