Let $n\ge 2$ be an integer. They are given $n + 1$ red points in the plane. Prove that there exist $2n$ circles $C_1 , C_2 , \ldots , C_n , D_1 , D_2 , \ldots , D_n$ such that: $\bullet$ $C_1 , C_2 ,\ldots , C_n$ are concentric. $\bullet$ $D_1 , D_2 ,\ldots , D_n$ are concentric. $\bullet$ For $k = 1, 2, 3,\ldots , n$ the circles $C_k$ and $D_k$ are disjoint. $\bullet$ For $k = 1, 2, 3,\ldots , n$ it is true that $C_k$ contains exactly $k$ red dots in its interior and $D_k$ contains exactly $n + 1 - k$ red dots in its interior.