Question 174
Let $k$, $n$ and $r$ be natural numbers with $r \lt n$. Quirin owns $k n + r$ black and $k n + r$ white socks. He wants to hang them on his clothesline in such a way that there are no $2 n$ consecutive socks of which $n$ are black and $n$ are white. Prove that Quirin can do this if and only if $r \geq k$ and $n \gt k + r$.