### 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?

# Hiking the Hill

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

Suppose the path is $x$ miles long. Then she takes $\frac{1}{2}x$ hours to walk up the hill, and another $\frac{1}{4}x$ hours to walk back down. Therefore, in $\frac{3}{4}x$ hours she walks a total distance of $2x$.

This means her average speed is $(2x) \div (\frac{3}{4}x) = \frac{8}{3} = 2\frac{2}{3}$ miles per hour.

This problem is taken from the UKMT Mathematical Challenges.

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