finding a quartic function over $R^n$ whose solution set is $\{0,1\}^n$

Question

I need to find a quartic function
$f: R^n \Rightarrow R$
such that $f \leq 0$ if and only if $x=\{0,1\}^n$
or:

$\{x \in R^n : f(x) \leq 0\} = \{0,1\}^n$

I'm really stuck on this and would appreciate any ideas on how to approach this.

Answer 1

Which scalar quadratic function would be zero in the point $0$ and positive everywhere else? Which scalar quadratic function would be $0$ in the point $1$ and positive everywhere else? What do you know about the product of these two functions? Generalize to multidimensional case by simply adding terms.