This is based on bonanova's puzzle Colorful Foreheads
Here's a game that goes as in the following
* There is a host with 14 stamps, 7 red and 7 blue. There are five players- A, B, C, D, and E.
* In the beginning, the host affixes two stamps to each of the 5 players' head. The remaining 4 stamps go into the host's pocket. Each player can see the stamps on the remaining 4 players, but can not see his own stamps nor the four in the host's pocket.
* Starting from A to E (and then looping back to A and so on), the host asks if each player definitively knows his stamps distribution (RR, BB, or RB). If the player does not know, the host goes on to the next player. No guessing is allowed.
* The game goes as follows
1st turn- player A: I do not know
2nd turn- player B: I do not know
3rd turn- player C: I do not know
4th turn- player D: I do not know
5th turn- player E: I do not know
Host- Alright, to help you, I'll now reveal two stamps from my pocket. *At this point, the host pulls out two of the four stamps in his pocket and shows everyone. The game then continues as before*
6th turn- Player A: I do not know.
Question- what is the longest possible number of turns required before a player definitely knows his color?