Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

What is the greatest number of squares you can make by overlapping three squares?

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .

Chris, Matt, Beh Sze, James and Jasmine all worked on this problem in a very systematic way.

We were very excited to find out about your ways of going about this investigation which we hadn't thought of before.

Alex and Tom have made good use of visualisations and their algebra to solve this problem

Bernard Bagnall discusses the importance of valuing young children's mathematical representations in this article for teachers.

You need to find the values of the stars before you can apply normal Sudoku rules.