### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### 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?

# Outside the Nonagon

##### Stage: 3 Short Challenge Level:

The exterior angles of a regular nonagon are $360^{\circ}\div 9 = 40^{\circ}$, whence the interior angles are $180^{\circ} - 40^{\circ}= 140 ^{\circ}$.

In the arrowhead quadrilateral whose rightmost vertex is X, three of the angles are $40^{\circ}$, $40^{\circ}$ and $360^{\circ} - 140^{\circ}=220^{\circ}$ and these add up to $300^{\circ}$.

So the angle at X is $60^{\circ}$.

[It is now posible to see that the entire nonagon can fit neatly inside an equilateral triangle and so the angle X is $60^{\circ}$ ]

This problem is taken from the UKMT Mathematical Challenges.
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