Combinations

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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?

Ben has five coins in his pocket. How much money might he have?

There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p in the sweet shop. What could each of the children buy with their money?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?