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How Many Ways Can You Arrange 128 Tennis Balls? Researchers Solve an Apparently Impossible Problem
Researchers have solved an apparently overwhelming physics problem involving some truly huge numbers [phys.org]. In summary, the problem asks you to imagine that you have 128 tennis balls, and can arrange them in any way you like. The challenge is to work out how many arrangements are possible and – according to the research – the answer is about 10250, also known as ten unquadragintilliard: a number so big that it exceeds the total number of particles in the universe.
Despite its complexity, this study also provides a working example of how "configurational entropy" might be calculated in granular physics. This basically means the issue of measuring how disordered the particles within a system or structure are. The research provides a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, to creating efficient artificial intelligence systems.
A bewildering physics problem has apparently been solved by researchers, in a study which provides a mathematical basis for understanding issues ranging from predicting the formation of deserts, to making artificial intelligence more efficient.
In research carried out at the University of Cambridge, a team developed a computer program that can answer this mind-bending puzzle: Imagine that you have 128 soft spheres, a bit like tennis balls. You can pack them together in any number of ways. How many different arrangements are possible?
The answer, it turns out, is something like 10250 (1 followed by 250 zeros). The number, also referred to as ten unquadragintilliard, is so huge that it vastly exceeds the total number of particles in the universe.
Far more important than the solution, however, is the fact that the researchers were able to answer the question at all. The method that they came up with can help scientists to calculate something called configurational entropy – a term used to describe how structurally disordered the particles in a physical system are.
Your configurational entropy problems are solved.
