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Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Can you find out in which order the children are standing in this line?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?