Mileva Marić (1875-1948) was a Serbian mathematician and Albert Einstein's first wife. There is a disparity of opinions about the magnitude of her contribution to Einstein's theories while they were married. Renowned mathematicians believe that she helped him solve mathematical and physics problems, in particular those concerning the theory of relativity or the explanation of the photoelectric effect, which granted him the Nobel Prize . What remains indisputable is that she had an important influence on Einstein's scientific work.

Notable mathematicians were astonished by how fast and easily Mileva solved complex mathematical problems.

You will read a mathematical problem related to the physics problems that she solved.

In nuclear fusion, a neutron crashes against the nucleus of an uranium atom. The nucleus absorbs the neutron and it emits three neutrons when it separates. Each one of these neutrons crashes against another uranium nucleus which, in turn, splits into three neutrons, and so on.

a) How many neutrons would the third collision produce? And the ninth one? And the fifteenth one? And the nth one?

b) How many collisions are necessary to produce a trillion neutrons, approximately?