It is a very nice riddle. I like that one, but I posed a very similar one on these forums. Mine involved hats, same situation, everybody have black hats and you need to determine which you have.
Here is the simplest situation. You have a hat and do not know that colour it is. Your opponent has a white hat and also does not know what colour it is for he cannot see it. The rule is at least 1 is black. How can you tell. Well, if you look at your opponet and see a white hat you immediately know that you must have a black hat, simple! Know what happens if you see a black hat. You reason like that, if I have a white hat my opponent see I have a white hat and thus immediately knows he has a black hat, but because he is silent (not saying anything) shows that he cannot deduce what color he has because I have black. Same situation here only extended to 100 people.