Working systematically

In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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?