A virus called a repellanoid has been implicated in a host of diseases. Biochemists have determined that it forms a cylinder, but they don't know the circumference of the cylinder. Here is what they know: There are five different strand sizes, which the scientists refer to by colors: aqua strands of length 4; blue, 5; crimson, 6; dark yellow, 7; and emerald, 8. Each ring of the cylinder consists of strands laid out end to end.
The biochemists have identified the following constraints: Taking the vertical direction to be along the length of the cylinder, if X is a ring and Y is the ring immediately above X, two above X, or three above X, then any vertical line between X and Y must touch a different color on X than on Y. That is, like repels like up to a distance of three. Of course, all the rings must have the same circumference. What is the smallest circumference of the cylinder?
This article was originally published with the title Repellanoids.