Question 17
Let $k$ be a positive integer. Show that for all $n \gt k$ the following is true:
There exist convex figures $F_1, \dots, F_n$ and $F$ such that no subset of $k$ figures chosen from $F_1, \dots, F_n$ completely covers $F$, but every subset of $k+1$ figures chosen from $F_1, \dots, F_n$ completely covers $F$.
There exist convex figures $F_1, \dots, F_n$ and $F$ such that no subset of $k$ figures chosen from $F_1, \dots, F_n$ completely covers $F$, but every subset of $k+1$ figures chosen from $F_1, \dots, F_n$ completely covers $F$.