Working systematically

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?

How many different phone numbers are there starting with a 3 and with at most two different digits?

Five equations and five unknowns. Is there an easy way to find the unknown values?

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

A Sudoku based on clues that give the differences between adjacent cells.

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?