The following problem is taken from the Theoretical Examination of the 44th annual International Chemistry Olympiad in 2012, a competition attended by four secondary school students from each of about 70 countries.

Graphene is a sheet of carbon atoms arranged in a two-dimensional honeycomb pattern. It can be considered as an extreme case of a polyaromatic hydrocarbon with essentially infinite length in two dimensions. Graphene has remarkable strength, flexibility, and electrical properties. The Nobel Prize for Physics was awarded in 2010 to Andre Geim and Konstantin Novoselov for groundbreaking experiments on graphene. A section of the graphene sheet is shown below.

The area of one hexagonal 6-carbon unit is ∼52400 pm². Calculate the number of π electrons in a tiny 25 nm × 25 nm sheet of graphene. For this problem you can ignore edge electrons (i.e., those outside the full hexagons in the picture).