TITLE: How to entertain a crowd with mathematics?
QUESTION [55 upvotes]: I am a high school student who follows a university level curriculum, and recently my teacher asked me to hold a short lecture to a crowd of about 100 people (mostly parents of my classmates and such, I'm not the only one to do something, other kids will sing and play the piano and such). I actually self-studied linear algebra and basic differential equations, but I felt that would be too boring (and the non-boring parts would be too difficult) to explain. I then decided to try and explain Euler's identity, since it looks so counter-intuitive and almost everyone knows $e$, $\pi$ and $i$. But I decided that it's undoable in like 10 minutes; only a handful of people would be able to follow it if I rush through it. 
So I guess my question is; Is there any mathematical 'thing' which is easy to follow and will blow the minds of the parents, literally? I literally want to see some heads pop. It doesn't need to be related to Linear Algebra/Calculus, but I need some interesting problems/theorems/formulas etc. which is understandable to the layman. I think this question might be useful to some other people on this site who are in a similair situation, and want to show math can be mindblowing. 
At the moment the best idea I've come up with is the birthday problem, I think my introduction would be pretty epic:
Me: Hello audience! Let me ask you a question: How big does a group of people have to be minimally if you want the chance of a pair sharing a birthday to be 100%?
Crowd: 367!
Me: Very good crowd! And approximately how many people for it to be 99%?
Crowd: Around 360?!
Me: Nope, 57.
Crowd: POP!
And I would continue to explain why, which is not hard at all.
Are the similair mathematical results which will blow the mind of a layman?

REPLY [2 votes]: You might want to "steal" a couple topic ideas from ViHart or Numberphile. 
Fractals is always interesting and easy to entertain since they are visual and you can use real-life objects (leafs, pineapples, etc) that people can easily relate to. 
Another topics suitable for entertaining crowds would be mathematic magic. You may instruct your audience to pick any random number, do some simple calculation and guess that whatever the number they picked, it all led to 42 (or some sort of that). Another common magic trick is the Number Guessing Game. Ask a member of the audience to pick a secret number, then ask if their number is in some cards containing a list of numbers, then guess what their secret number is. If you then follow these magic tricks by explaining how and why the trick works, it could be educational as well as entertaining.
Another possible topic is the Seven Bridges of Königsberg for Graph Theory. You can start by saying you want to play a game, involve your audience by asking them to try solving the bridges with maps that are actually solvable (you may want to offer them a small prize for answering), then after the audience felt comfortable with the game, present them with an unsolvable bridges. Follow up with explaining of why it's unsolvable.
Keep these in mind when entertaining an audience:

Tell a story, not lessons.
Involve the audience.
Keep it simple. You want audiences to be able to follow what you are doing.
Use daily objects that the audience can relate to.
Use visuals.
Keep an element of surprise.
Rehearse and practice. A lot. You have to know your topic inside out, more than just what you're planning to talk about. Practice with a test audience if necessary.