Maths secrets of M&Ms revealed

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.

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


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BBC NEWS | Science/Nature | Maths secrets of M&Ms revealed