What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
Each of the following shapes is made from arcs of a circle of radius $r$. What is the perimeter of a shape with $3$, $4$, $5$ and $n$ "nodes"?
What happens when $n$ is very large?
Explain the relationship between your answers and the perimeter of the original circle.