Working systematically

If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

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?

How many triples of points are there in this 4×4 array that lie on a straight line?

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?

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?

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?

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?