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New Neighborhood
Captain Cohen started to talk about Graham’s number, an exuberantly large number. The number was so large, that it could not be contained in the observable universe.

“Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured complete subgraph on four coplanar vertices?” asked Cohen.

“Huh?” Theo looked at him like an idiot. He was overwhelmed, “Let me get a pen and paper…” Theo tried to find it.

“Won’t work. You cannot write the number on a piece of paper,” Cohen said, “In our observable universe, there is not enough space to write the number on.”

While the UEC Expeditionary members finished exploring 500 cubic light years area of space, they had to settle down. There were not enough supplies with them to go on like that forever. Soon, they had to find a new planet, meet
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