Let $\vartheta_1,...,\vartheta_n$ be independent, uniformly distributed, random variables in the unit interval $[0,1]$. Define h(x)\equal{} \frac1n \# \{k: \; \vartheta_k$x_0 \in (0,1)$ such that h(x_0)\equal{}x_0, is equal to 1\minus{} \frac1n. G. Tusnady