Question: > 
> There is a group of finite aliens on a spaceship. Show that there are at least $2$ aliens who know the same number of aliens on the spaceship. 
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I was given a hint, and that was to use the pigeonhole principle. I think I can visually see it but I am unsure how to show it.

Answer: 
**Hint:**

There are $N$ aliens, and assume one of the alien knows $K$ aliens. $(N>K)$

Can each alien know **distinct** number of aliens? 

Assume $A\_1$ knows ${A\_2,A\_3 \dots A\_{K+1}}$, now that $A\_2$ knows $K$ aliens, the aliens who he knows also knows him.(Though confusing, its the fact -evil laugh-)
An alien can know between $0$ and $n-1$ aliens. That is $n$ possibilities. If one alien knows everyone else, then there is no one who doesn't know any one. And the other way around. So possibilities $0$ and $n-1$ are mutually exclusive. So we are down to $n-1$ possibilities for each alien to know others.

So if there are $n$ aliens and $n-1$ possibilities of knowing others, with then at least $2$ aliens exist who know the same number of aliens on the spaceship.