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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 $n=2$, $f(n)=f(2)=4$:

enter image description here

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!

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

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!

A housewife is waiting for guests and has 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

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!

minor typo + added (fair-division) tag; feel free to remove it if (for some reason) the tag is nt a good fit for the question
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Martin Sleziak
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A hausewifehousewife 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

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!

A hausewife 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

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!

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

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!

Source Link

Dividing a cake between $n-1$, $n$, or $n+1$ guests

A hausewife 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

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!