Erdős Problem 36

This example calculates the value of $M 1$. The set is $\{1, 2\}$, so the only partition is $A = \{1\}, B = \{2\}$ (or vice versa). The possible differences are $1 - 2 = -1$ and $2 - 1 = 1$. The Overlap for $k=-1$ is 1 (if $A=\{1\}, B=\{2\}$) and for $k=1$ also 1 (if $A=\{2\}, B=\{1\}$ ). The MaxOverlap is $1$, since the Overlap is $0$ for other $k$. Thus, $M 1 = 1$.