Problem Pictures 1 cover

This picture is taken from the Problem Pictures resource of photographs with activities for mathematics teaching.

If you purchase this resource the photographs are available in higher resolution and there are additional pages containing hints and solutions.

Box of jelly beans

Box of jelly beans

Each compartment in this box contains six jelly beans of the same flavour. They are arranged in two layers of three beans. There is a different flavour in each compartment.

How many different flavours are there in the box? How many beans are there altogether?

Jelly beans are sold in "40 official flavours". Suppose that the jelly bean company asks you to design a similar box that could hold all 40 flavours. Is this possible?