Can you find rectangles where the value of the area is the same as the value of the perimeter?

Charlie has moved between countries and the average income of both has increased. How can this be so?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Can you rearrange the cards to make a series of correct mathematical statements?

How many different cubes can be painted with three blue faces and three red faces? A boy (using blue) and a girl (using red) paint the faces of a cube in turn so that the six faces are painted. . . .

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis. How many paths are there for 4 steps, for 6 steps, for 8 steps?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

We received good solutions to this problem, many offering insights into the properties of the numbers that were paired off.

Kirsti Ashworth, an NRICH Teacher Fellow, talks about her experiences of using rich tasks.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Each clue number in this sudoku is the product of the two numbers in adjacent cells.