The Interactive Card Problem (Hard)

Inspired by  http://www.khanacademy.org/math/brain-teasers/v/alien-abduction-brain-teaser

This is a challenge that will make you think, and can be done and tested with a group of people. All you need is your mind and possibly a group of willing people, cards, and tape.

The objective is to teach problem solving, and practice creating and applying mathematical systems.

Step 1: Materials

You will need-

-a group of preferably more than 5 people
-tape (for taping cards to peoples' backs)
-playing cards
-a room preferably without mirrors and reflective surfaces
-paper and pencil