### 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?

# Pyramidal N-gon

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

The base of the pyramid has $n$ edges, so also has $n$ vertices around the base. This then means that there are $n$ edges around the base (in red) of the pyramid and $n$ that meet at the apex (in black).
This means there are $2n$ edges in total.

There are also $n$ faces that meet at the apex of the pyramid, and one more for the base, so a total of $n+1$ faces.

Therefore the difference is $2n - (n+1) = n-1$.

This problem is taken from the UKMT Mathematical Challenges.
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