### 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?

# As Long as Possible

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

$14 \; \text{cm}$. The length of $AD$ must be less than $15 \; \text{cm}$, since $15 \; \text{cm}$ would be its length if all four points lay in a straight line. However, by making angles $ABC$ and $BCD$ close to $180^{\circ}$, $AD$ can be made close to $15 \; \text{cm}$ in length.

As the length of $AD$ is a whole number of centimetres, its maximum value, therefore is $14\; \text{cm}$

This problem is taken from the UKMT Mathematical Challenges.
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