### 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:

Sarah walks uphill at an average of 2 miles per hour, and downhill at an average of 4 miles per hour.
She goes for a 6 mile hike up a hill, and then returns downhill by the same route.

What is Sarah's average speed in miles per hour for the whole journey?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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