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Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

What do you notice about the sum of two identical triangular numbers?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.