 
Summary: Tomaso Aste and Tiziana Di Matteo
In the year 2000, exactly one hundred years after David Hilbert posed
his now famous list of 23 open problems, The Clay Mathematics Insti
tute (CMI) announced its seven Millennium Problems. (http://www.
claymath.org/millennium). The Gazette has asked leading Australian
mathematicians to put forth their own favourite `Millennium Problem'.
Due to the Gazette's limited budget, we are unfortunately not in a posi
tion to back these up with sevenfigure prize monies, and have decided on
the more modest 10 Australian dollars instead.
In this final instalment, Tomaso Aste and Tiziana Di Matteo will explain
their favourite open problem that should have made it to the list.
In this note we describe our favourite problem in discrete geometry: how many equal spheres
can be packed inside a larger sphere?
This problem is related with the long standing `greengrocers dilemma': which is the most
spaceefficient way of placing vegetables in a market stand? Such a dilemma might have
intrigued a few greengrocers (Fig. 1) but it has certainly attracted several mathematicians
becoming one of the bestknown problems in discrete geometry. This problem is often
referred as the Kepler conjecture and it was included at the 18th place in the Hilbert's list.
Figure 1. The greengrocers dilemma: which is the most spaceefficient way of
placing vegetables on a market stand?
