TITLE: Giving a math talk with no blackboard or projector
QUESTION [12 upvotes]: I need to give a math talk to a group of undergraduates.  I am asking for advice because this talk will take place at a department picnic and there will be no blackboard or projector.  I would like to talk about graph theory/combinatorics and I could conceivably use props or handouts.  Does anybody have any suggestions?

REPLY [2 votes]: Thank you to everybody for the great suggestions.  I have decided what to do (see below) and I'll let you know how it goes after the picnic next week.  I was inspired by the audience participation aspect of Josephus problem suggestion.
I will ask for a group of say 11 volunteers and ask them to shake hands with each other so that they all shake exactly three hands.  Of course this is impossible and I will explain why.  I may ask them if they can do this with an even number of people and have them try to come up with the construction.  
Next I will describe a triple handshake (a group hug might be awkward...) and ask a group of 7 volunteers if they can do triple handshakes so that every pair of people are involved in exactly one triple handshake.  Of course this is challenging without thinking about it for a while, but I will show them how to do it after they try.  Then I will ask them if this can happen with 8 people.  Again this is impossible and I will explain why.  Now that we know there can be no "special triplehandshake system" (STS) on an even number of vertices I will explain why it can't happen with some odd numbers, like 11 for instance.