Find your way through the grid starting at 2 and following these operations. What number do you end on?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

I cut this square into two different shapes. What can you say about the relationship between them?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

There are six numbers written in five different scripts. Can you sort out which is which?

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Can all unit fractions be written as the sum of two unit fractions?

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

What fractions can you divide the diagonal of a square into by simple folding?

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Can you find the area of the central part of this shape? Can you do it in more than one way?

Match the charts of these functions to the charts of their integrals.

Have a look at the different ways in which the solution to this problem was expressed.

We received many extremely well-explained solutions to this problem. Read about the different ways it was approached.

We received many correct solutions to this problem. However, all the solutions have not been found yet. Can you find any more?

We had some interesting explanations and comments on this unusual way of representing division.

Ideas to support mathematics teachers who are committed to nurturing confident, resourceful and enthusiastic learners.

Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!