Posts filed under ‘The Twenty People at a Party Puzzle’

The Twenty People at a Party Puzzle

Suppose there are twenty people in a room.

If Alice and Bob are any two of them, and Alice knows Bob, then you may assume that Bob knows Alice. Furthermore, if Alice does not know Bob then, likewise, Bob does not know Alice.

Now, any individual among these twenty may know nobody else, or some but not all of the others, or know everybody in the room.

However, what might strike you as amazing on first thought is the fact that all twenty cannot each know a different number of people in the room. Put another way, there are at least two in the room who know exactly the same number of people.

Can you reason out why this must be?

In Code: A Mathematical Journey


August 9, 2010 at 2:42 pm Leave a comment