The Vander Vareden Problem

A 1946 construction by Felix Berente has found a wide range of applications. In the final days of 2020, while out for a leisurely walk with his wife and children, Green suddenly had an insight. He realized that if you choose just the right size and quantity of circles,. then the scattered blue circles will thoroughly disrupt the red territory without creating significant opportunities for blue sequences to form. This makes it possible to string many beads without creating any long red sequences, or any blue sequences at all.