### 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?

# Regional Division

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

Some trial and error will produce a solution like that on the right, where there are $9$ different areas enclosed.

To see that this is indeed the maximum, there is always one central region ($9$ on the diagram), and then the others must be separated from this by one of the sides of one of the rectangles. Each side can only separate one region, and as there are a total of $8$ sides, this means at most $9$ regions in total.

This problem is taken from the UKMT Mathematical Challenges.
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