14 Divisors

What is the smallest number with exactly 14 divisors?

Summing Consecutive Numbers

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?

Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Arclets

Stage: 3 Challenge Level:

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.