Working systematically

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

Can you swap the black knights with the white knights in the minimum number of moves?

From this sum of powers, can you find the sum of the indices?

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?