Working systematically

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Can you find a way to identify times tables after they have been shifted up or down?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Use the clues about the shaded areas to help solve this sudoku