Maths secrets of M&Ms revealed

The discovery may help development of new materials

M&M sweets pack together more densely than perfect spheres when randomly jumbled in a container, scientists say.

Same-sized spheres were previously thought to have the highest "packing fraction" - the relative density of objects when shoved in a container.

US scientists compared the packing densities of M&Ms with those of ball bearings in different containers.

Computer simulations confirmed the findings, which the team report in the current issue of the journal Science.

Salvatore Torquato of Princeton University in New Jersey, US, and colleagues used a 9cm by 9cm square box and three round flasks of different sizes to investigate the conundrum.

The researchers filled these containers with M&M sweets and determined the packing fractions for them. They measured these for both the "regular" and "mini" varieties of the chocolates.

Computer simulation

Then they compared these values with those obtained when the same containers were filled with 3.1mm ball bearings.

Computer simulations helped the scientists study the phenomenon

The results showed that M&Ms packed at higher densities than ball bearings in all containers tested.

To better understand the principle, the researchers developed a computer simulation that allowed them to generate any shape and test its packing density.

When they stretched the M&M shape so it looked elliptical from the top as well as from the side, like an almond, it achieved a density approaching the highest possible packing fraction of 0.74.

The researchers say these amazing properties are down to the fact that more contacts per ellipsoid particle are needed to ensure jamming in a container. And of course, forming more contacts requires denser packing.

The question of how particles randomly pack together has been a persistent scientific problem for hundreds of years.

The problem of how much grain a barrel could hold was of economic importance to traders throughout history.

The scientists say their work is important to anyone involved in the study of particle packing.

Materials scientists, for example, make high-performance ceramics by fusing powders made of tiny particles. A more tightly packed powder with many contact points could yield a less porous ceramic, say the researchers.