Brain Teasers

1. There are 26 towns and Air Chennai connects every pair of these towns by an air route. How may air routes are there?

2. The island of Elbonia have a rather eccentric postal system. Postage for an item can be anything from 1 dinar to 15 dinari, and you must use exact postage. Frustratingly, there is only space on the envelopes in Elbonia to attach a maximum of three stamps. What is more, they only have three different denominations of stamps. Can you work out what they are?

3. You are given a 10x10x10 cube composed of one thousand 1x1x1 "mini-cubes" glued together. If the outer most layer falls off, how many "mini-cubes" would have fallen off?