Which of these triangular jigsaws are impossible to finish?

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

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

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

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?

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

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

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.

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

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

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