Puzzles for Programmers and Pros

1.4. Information Gain

The well-known and always well-dressed game show host Jeff Nicholas has approached Jordan and his friends Ariana, Bob, Caroline, David, and Ellen with a contest proposition. Jordan and the five are the leading lights of the omniheurist club, a group of outstanding puzzle solvers.

"Our contest is live. I will blindfold your friends, then put a hat on each of them bearing a number between 1 and 10 (more than one person may have the same number) and lead them into a televised game room. Once they have arrived, I will arrange them in a circle in an order that I choose and then replace each blindfold by very dark but non-reflecting sunglasses to eliminate the possibility of eye signals.

"You and the audience will see them in the game room and the numbers on their heads via the television monitor, but they won't be able to see you. I will be holding one blue ticket and one red ticket. You can ask me to deliver one ticket to one of the five. That's all you can do. No knocking on the window or your team will be disqualified.

"The mathematicians may not speak or signal one another in any way, or the entire team will be disqualified. (Obviously, I won't help them in any way other than delivering the ticket.) They will, however, see to whom the ticket is being delivered ...