This one is tougher....?

Question

4) There are 13 men in a closed room. The man that has placed them there has given them each a ring box with either a bean or a diamond in it. These men can show every other person their box, BUT CAN NOT SEE WHAT THEY HAVE THEMSELVES! There is NO communicating between the men (no sign language NOTHING). The man that has placed them there said that in order to live they must get all the people with the diamonds in their box out of the room and all the people with the bean in their box in the room. (ex. Chance one: all of them exit the room). Each time they are wrong the man who has placed them there will let them know they are wrong and they all must keep trying. The man has given them 11 chances. You must assume that all the men are thinking the same STRATEGY! The men in the room happen to get it in 7 tries! Explain the strategy they used to have done this.

Answer 1

I don't know how they did it in 7, but I could detail a strategy for them to do it in 1.

Strategy:
1) The 13 men pair up in groups of 2, obviously with 1 being left out. Call him #13. So there are 6 pairs.

2) In each pair, the men look at each other's boxes. If they see a bean, then begin to leave the room. If they see a diamond, they remain putt. So there are 3 possibilities:

2A) Bean, Diamond.
In this case the diamond leaves and the bean remains.
2B) Diamond, Diamond.
In this case, they both remain.
2C) Bean, Bean
In this case, they both begin to leave.

3) If they both begin to leave, then they know that they both have beans, in which case they stay in the room.
If, after 5 seconds, they both make no motion to leave, they know that they both have diamonds, in which case they both leave.
NOTE this is not considered communication, just part of the strategy they are all thinking.

4) One of the guys who remain (a bean) goes to #13 and looks at his box. If he sees a diamond, he goes to a specific corner of the room. If he sees a bean, he goes back together with the rest of the guys. #13 will now know whether to leave or stay.
Again, this is part of the strategy they all know.

In 1 try, all the diamonds leave the room, and all the beans remain.

Answer 2

wow.. keep the question shorter...