### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# 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.