This picture is taken from a CD-ROM of photographs with activities for mathematics teaching. Published as Mathematical World in America and as Problem Pictures in the UK, Europe and Australasia.

Box of jelly beans

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

How many different flavors 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 flavors. Is this possible?

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