"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

The challenge for you is to make a string of six (or more!) graded cubes.

How many different symmetrical shapes can you make by shading triangles or squares?

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Find curves which have gradients of +1 or -1 at various points

We had some good solutions to this problem. I wonder whether there are any other possibilities?

Many of you worked out the rules behind these lights. Have a look at the solutions that were sent in.

Herschel figured out an experiment which might have led to the graph, and sent us a skilful analysis of the data.

The black box was cracked by several solvers in a great show of ingenuity and determination.

What might your first lesson with a new class look like? In this article, Cherri Moseley makes some suggestions for primary teachers.

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

In this article, read about the thinking behind the September 2010 secondary problems and why we hope they will be an excellent selection for a new academic year.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

A task which depends on members of the group noticing the needs of others and responding.

Weekly challenges are here for NRICH! To celebrate this event, we've collected a set of 20 essential problems for you to try.

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.