Here's for a real question:
There is a big group of people on a field and they randomly get assigned hats, either blue or red ones. They can not see what colour hat they are wearing and they are not allowed to communicate in any way with the others. No gestures, no pointing, no nothing. How can they devide so that all of the red ones are on one side of the field and the blues are on the other side?
I've heard this one, but in a different format. However, I see it as a way for a person to easily cop out with an answer to a defenseless question: "people" is plural for "person"; which means one could simply answer, "well there are only 2 people in the field...and they're really big...each go their own separate ways...the question didn't clarify number of people in the field, just 'big group' , which isn't clear enough as to exactly how many, odd or even..." This answer isn't necessarily wrong, but the question actually has it's "special" answer, so my bull-shat response, isn't necessarily this question's sought after answer.
May need specific numbers to make this truly a "red-hat, blue-hat" brain teaser...