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.

Comments