Pigeonholing finite aliens on a spaceship

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.

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 1

HINT: Let $n$ be the number of aliens on the ship. As noted in the comments, you must assume that $n\ge 2$. Suppose that A is an alien on the ship; how many of the others can it know? The largest possible answer is $n-1$, and the smallest is $0$.

• How many possibilities is that?
• Is it actually possible for one of the aliens to know $n-1$ of the others and another to know $0$?

Answer 2

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-)