MathDB

In a virtually-made world, each citizen, which is assumed to be a point (i.e. without area) and labelled as

1, 2, ...

. To fight against a pandemic, these citizens are required to get vaccinated. After they get vaccinated, they need to be observed for a period of time. Now assume the location that the citizens get observe is a circumference with radius

\frac{1}{4}

on the plane. For the safety reason, it is required for distance between

m

-th citizen and

n

-th citizen

d_{m, n}

satisfying the following:

(m+n)d_{m, n}\geq 1

Here what we consider is the distance on the circumference i.e. the arc length of minor arc formed by two points. Then (a) Choose one of the following which fits the situation in reality. A. The location for observation can mostly have

8

citizens. B. The location for observation can have the upper limit on the number of citizens which is larger than

8

. C. The location for observation can have any number of citizens. (b) Prove your answer in (a).

Problem Statement