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14 Divisors

What is the smallest number with exactly 14 divisors?

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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?

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Do you know a quick way to check if a number is a multiple of two? How about three, four or six?


Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Each of the following arclets is made from arcs of a circle of radius r.


What is the perimeter of an arclet 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.