Secret sharing. Suppose we have $N$ people. We want any $k+1$ of them to be able to launch a missile attack, but no $k$ of them to have this power.

Solution: Choose some large prime $p$ and a random polynomial $f(t)$ of degree $k$ with coefficients in $\mathbb{Z}/p$. Tell person $1$ the value of $f(1)$, person $2$ the value of $f(2)$ and so forth. (Also, everyone knows what $p$ is.) Set up the missiles to only launch when $f(0)$ is input. Any $k+1$ people can use the Chinese remainder theorem to compute $f$, and hence $f(0)$; any $k$ people do not have enough data to constrain $f(0)$ in any way.