Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

How much of the square is coloured blue? How will the pattern continue?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Can you describe this route to infinity? Where will the arrows take you next?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

A collection of short Stage 3 and 4 problems on Reasoning, Justifying, Convincing and Proof.

There are lots of different methods to find out what the shapes are worth - how many can you find?

When is it impossible to make number sandwiches?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Can you find the values at the vertices when you know the values on the edges?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Can you create a Latin Square from multiples of a six digit number?

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

Can you fit polynomials through these points?

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Which of these triangular jigsaws are impossible to finish?

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.