Question

Suppose $2016$ points of the circumference of a circle points are coloured red and the remaining points are coloured blue. Find the minimum possible value of a natural number $n$, for which there exists a regular $n$- sided polygon whose all vertices are blue.

• A. $5$
• B. $3$
• C. $6$
• D. Not possible

Answer 1

Answer: (B)

$3$

Given that there are $2016$ red colored points on the circumference of circle and $n$ blue color points on the circumference of circle.

In order to form a $n$-sided regular polygon, the number of red colored points between any two adjacent blue colored points must be same on the circle.

Therefore $n$ should divide $2016$

If $n=2$ , then polygon is not possible. In order to form closed polygon, minimum $3$ vertices are required

We can see that $2016$ is divisible by $3$

Therefore minimum possible value of $n$ is $3$

So the correct option is $B$